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Mathematical function
In mathematics, the Riesz function is an entire function defined by Marcel Riesz in connection with the Riemann hypothesis, by means of the power series
Riesz_function
Hungarian mathematician
Marcel Riesz (Hungarian: Riesz Marcell [ˈriːs ˈmɒrt͡sɛll]; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation
Marcel_Riesz
Statement about linear functionals and measures
In mathematics, the Riesz–Markov–Kakutani representation theorem relates linear functionals on spaces of continuous functions on a locally compact space
Riesz–Markov–Kakutani representation theorem
Riesz–Markov–Kakutani_representation_theorem
function Complete Fermi–Dirac integral, an alternate form of the polylogarithm. Dilogarithm Incomplete Fermi–Dirac integral Kummer's function Riesz function
List of mathematical functions
List_of_mathematical_functions
Theorem about the dual of a Hilbert space
The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes
Riesz_representation_theorem
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Theorem on operator interpolation
mathematical analysis, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is
Riesz–Thorin_theorem
Generalized function whose value is zero everywhere except at zero
the space of all compactly supported continuous functions φ {\displaystyle \varphi } which, by the Riesz representation theorem, can be represented as the
Dirac_delta_function
Function spaces generalizing finite-dimensional p norm spaces
Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional
Lp_space
Mathematical theorem
integrable functions. The theorem was proven independently in 1907 by Frigyes Riesz and Ernst Sigismund Fischer. For many authors, the Riesz–Fischer theorem
Riesz–Fischer_theorem
Type of singular integral operator
convolution of one function with another function having a singularity at the origin. Specifically, the Riesz transforms of a complex-valued function ƒ on Rd are
Riesz_transform
Potential in mathematics
mathematics, the Riesz potential is a potential named after its discoverer, the Hungarian mathematician Marcel Riesz. In a sense, the Riesz potential defines
Riesz_potential
Function on an integer n which is log(p) if n equals p^k and zero otherwise
terms, and are only readily visible when y < 10−5. The Riesz mean of the von Mangoldt function is given by ∑ n ≤ λ ( 1 − n λ ) δ Λ ( n ) = − 1 2 π i ∫
Von_Mangoldt_function
Point to which functions converge in analysis
"dubious lament". At the 1908 international congress of mathematics F. Riesz introduced an alternate way defining limits and continuity in concept called
Limit_of_a_function
Monotone maps have countable discontinuities
explained in Riesz & Sz.-Nagy (1990), every non-decreasing non-negative function F can be decomposed uniquely as a sum of a jump function f and a continuous
Discontinuities of monotone functions
Discontinuities_of_monotone_functions
Set of functions between two fixed sets
functional analysis deals with their relationships, such as the Riesz representation theorem, the Riesz–Thorin theorem, the Gagliardo–Nirenberg interpolation inequality
Function_space
circle. This result, the Herglotz-Riesz representation theorem, was proved independently by Gustav Herglotz and Frigyes Riesz in 1911. It can be used to give
Positive_harmonic_function
Summability method used in harmonic analysis
The Bochner–Riesz mean is a summability method often used in harmonic analysis when considering convergence of Fourier series and Fourier integrals. It
Bochner–Riesz_mean
Integral transform and linear operator
theorem), as well as work by Riesz, Hille, and Tamarkin One form of the Riemann–Hilbert problem seeks to identify pairs of functions F+ and F− such that F+
Hilbert_transform
Rational number sequence
(depending on ε) such that |R(x)| < Cεxε as x → ∞. Here R(x) is the Riesz function R ( x ) = 2 ∑ k = 1 ∞ k k ¯ x k ( 2 π ) 2 k ( B 2 k 2 k ) = 2 ∑ k =
Bernoulli_number
Partially ordered vector space, ordered as a lattice
a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces
Riesz_space
Special mathematical functions defined on the surface of a sphere
of ΔSn−1. In particular, an application of the spectral theorem to the Riesz potential Δ S n − 1 − 1 {\displaystyle \Delta _{S^{n-1}}^{-1}} gives another
Spherical_harmonics
Vector space of functions in mathematics
Almeida and S. Samko, "Characterization of Riesz and Bessel potentials on variable Lebesgue spaces", J. Function Spaces Appl. 4 (2006), no. 2, 113–144) and
Sobolev_space
Type of vector space in math
David Hilbert (after whom they are named), Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations
Hilbert_space
Mathematical function
for all x {\displaystyle x} in H . {\displaystyle H.} It follows from the Riesz representation theorem that any symmetric (defined as a ( x , y ) = a (
Coercive_function
Real function with finite total variation
Radon measure by the Riesz–Markov–Kakutani representation theorem. If the function space of locally integrable functions, i.e. functions belonging to L loc
Bounded_variation
Well-quasi-ordering of finite trees
application of the theorem gives the existence of a fast-growing TREE function. TREE(3) is one of the largest simply defined finite numbers, dwarfing
Kruskal's_tree_theorem
Concept within complex analysis
H^{p}} are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923), who named them after G
Hardy_space
Class of mathematical functions
measure in D {\displaystyle D} . This is called the Riesz representation theorem. Subharmonic functions are of a particular importance in complex analysis
Subharmonic_function
Many-body of charged particles
Physics for their work on this phase transition. Define the function (Coulomb kernel, or Riesz kernel) g s ( x ) = { − log | x | if s = 0 , 1 s | x |
Coulomb_gas
physicist (Docent 1926-30) Marcel Riesz (1886-1969), mathematician (Riesz function, Riesz theorems, Riesz mean, Riesz potential) (Professor from 1926)
List of Lund University people
List_of_Lund_University_people
Concept in mathematics
a + 2 π ) {\displaystyle [a,a+2\pi )} unless it is the zero function. The Fejér-Riesz theorem states that every positive real trigonometric polynomial
Trigonometric_polynomial
Nonlocal mathematical operator
vector-valued Riesz transform. For a function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } , the j {\displaystyle j} -th Riesz transform
Fractional_Laplacian
points). Hence, in particular, it is generally not locally compact. The Riesz–Markov–Kakutani representation theorem gives a characterization of the continuous
Space of continuous functions on a compact space
Space_of_continuous_functions_on_a_compact_space
Type of metric geometry
Frigyes Riesz and Hermann Minkowski. The formalization of Lp spaces, which include taxicab geometry as a special case, is credited to Riesz. In developing
Taxicab_geometry
Mathematics lemma in functional analysis
In mathematics, Riesz's lemma (after Frigyes Riesz) is a lemma in functional analysis. It specifies (often easy to check) conditions that guarantee that
Riesz's_lemma
Conjecture on zeros of the zeta function
examples are as follows. (Others involve the divisor function σ(n).) The Riesz criterion was given by Riesz (1916), to the effect that the bound − ∑ k = 1 ∞
Riemann_hypothesis
Generalized average used for summability
Riesz mean should not be confused with the Bochner–Riesz mean or the Strong–Riesz mean. Given a series { s n } {\displaystyle \{s_{n}\}} , the Riesz mean
Riesz_mean
Theorem on extension of bounded linear functionals
of continuous functions on an interval was proved earlier (in 1912) by Eduard Helly, and a more general extension theorem, the M. Riesz extension theorem
Hahn–Banach_theorem
Mathematical transform that expresses a function of time as a function of frequency
{\displaystyle L^{p}(\mathbb {R} )} by Riesz–Thorin interpolation, which amounts to decomposing such functions into a fat tail part | f | ≤ 1 {\displaystyle
Fourier_transform
Differential operator in mathematics
values of the function on all of R n {\displaystyle \mathbf {R} ^{n}} . The inverse of the fractional Laplacian is closely related to the Riesz potential
Laplace_operator
Method for estimating new data within known data points
operators". The classical results about interpolation of operators are the Riesz–Thorin theorem and the Marcinkiewicz theorem. There are also many other
Interpolation
mathematics, the notions of an absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
Normed vector space that is complete
Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central
Banach_space
Mathematical concept
by Marcel Riesz. The classical techniques include the use of Poisson integrals, interpolation theory and the Hardy–Littlewood maximal function. For more
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
Branch of functional analysis
the ring of polynomial functions. Extending by continuity defines f(T) for a continuous function f on the spectrum of T. The Riesz-Markov theorem then allows
Borel_functional_calculus
Integral transform
when applied to analytic functions. It was generalized to arbitrary dimensions by Marcel Riesz, who introduced the Riesz potential. The Riemann-Liouville
Riemann–Liouville_integral
explicites' de la théorie des nombres premiers", Comm. Lund (vol. dédié a Marcel Riesz) (1952) 252–265; Collected Papers II A. Weil, "Sur les formules explicites
Weil's_criterion
Method of mathematical integration
complete and careful presentation of the theory. Good presentation of the Riesz extension theorems. However, there is a minor flaw (in the first edition)
Lebesgue_integral
Topics referred to by the same term
function spaces Lp and ℓ p {\displaystyle \ell ^{p}} L-space (topology), a hereditarily Lindelöf space The Banach lattice, an abstract normed Riesz space
L-space
The M. Riesz extension theorem is a theorem in mathematics, proved by Marcel Riesz during his study of the problem of moments. Let E {\displaystyle E}
M._Riesz_extension_theorem
Topological vector spaces
Schwartz (similar to the Riesz representation theorem), every distribution which is non-negative on non-negative functions is of this form for some (positive)
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
Area of mathematics
founded the modern school of linear functional analysis further developed by Riesz and the group of Polish mathematicians around Stefan Banach. In modern introductory
Functional_analysis
p_{2},\ldots ,p_{n}} is called an e-simple function. The Freudenthal spectral theorem states: Let E be any Riesz space with the principal projection property
Freudenthal_spectral_theorem
Area of mathematical analysis
Riesz transforms, which are connected with the derivatives of harmonic and Newtonian potentials. One ingredient is Hardy–Littlewood maximal function.
Harmonic_analysis
Mathematics of real numbers and real functions
properties of the real numbers – such generalizations include the theories of Riesz spaces and positive operators. Also, mathematicians consider real and imaginary
Real_analysis
Expressing a measure as an integral of another
Radon–Nikodym theorem by proving the Freudenthal spectral theorem, a result in Riesz space theory; this contains the Radon–Nikodym theorem as a special case
Radon–Nikodym_theorem
Mathematical series
given in Section 27.4 of the NIST Handbook of Mathematical Functions/ Hardy, G. H.; Riesz, M. (1915). The General Theory of Dirichlet's Series. Cambridge
Dirichlet_series
Gives condition for a set of functions to be relatively compact in an Lp space
theorem (the names of Riesz or Weil are sometimes added as well) gives a necessary and sufficient condition for a set of functions to be relatively compact
Fréchet–Kolmogorov_theorem
Result in measure theory
densities in 1947. The result is a special case of a theorem by Frigyes Riesz about convergence in Lp spaces published in 1928. David Williams (1991)
Scheffé's_lemma
In mathematical analysis, the rising sun lemma is a lemma due to Frigyes Riesz, used in the proof of the Hardy–Littlewood maximal theorem. The lemma was
Rising_sun_lemma
Objects that generalize functions
function Homogeneous distribution Hyperfunction Laplacian of the indicator Linear form Malgrange–Ehrenpreis theorem Pseudodifferential operator Riesz
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
In functional programming
(V\rightarrow K)} . If this is the inner-product of a Hilbert space, the Riesz representation theorem ensures this is an isomorphism. The partial application
Partial_application
In functional analysis, a Hilbert space
{\displaystyle H} from which the RKHS takes its name. More formally, the Riesz representation theorem implies that for all x {\displaystyle x} in X {\displaystyle
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Shape containing unit line segments in all directions
Kakeya conjecture is closely related to the restriction conjecture, Bochner-Riesz conjecture and the local smoothing conjecture. In February 2025, a claimed
Kakeya_set
Theorem about inclusions between Sobolev spaces
{\displaystyle Rf} is the vector-valued Riesz transform, cf. (Schikorra, Spector & Van Schaftingen 2017). The boundedness of the Riesz transforms implies that the
Sobolev_inequality
Function from sets to numbers
In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes
Set_function
the idea appeared implicitly in earlier work by Johansson, Frigyes Riesz, Marcel Riesz, Torsten Carleman, Alexander Ostrowski and Gaston Julia. The connection
Harmonic_measure
Hungarian mathematician
Frigyes Riesz, he made the University of Szeged a centre of mathematics. He also founded the Acta Scientiarum Mathematicarum journal together with Riesz. Haar
Alfréd_Haar
Hungarian mathematician
mathematician. Szőkefalvi-Nagy collaborated with Alfréd Haar and Frigyes Riesz, founders of the Szegedian school of mathematics. He contributed to the
Béla_Szőkefalvi-Nagy
Mathematical theory by discovered by Józef Marcinkiewicz
similar to the Riesz–Thorin theorem about linear operators, but also applies to non-linear operators. Let f be a measurable function with real or complex
Marcinkiewicz interpolation theorem
Marcinkiewicz_interpolation_theorem
Branch of mathematical analysis
In addition, these distributions are geometric stable distributions. The Riesz derivative is defined as F { ∂ α u ∂ | x | α } ( k ) = − | k | α F { u }
Fractional_calculus
Mathematical integral
gamma function which cancels with the gamma from Ramanujan's Master Theorem. A closely related integral frequently occurs in the discussion of Riesz means
Nørlund–Rice_integral
Generalization of the Riemann integral
original formulation of F. Riesz's theorem which represents the dual space of the Banach space C[a,b] of continuous functions in an interval [a,b] as Riemann–Stieltjes
Riemann–Stieltjes_integral
basis of H2(∂Ω) consisting entirely of the restrictions of functions in A(Ω), then a Riesz–Fischer theorem argument shows that S ( z , ζ ) = ∑ i = 1 ∞
Szegő_kernel
Branch of functional analysis
L(X) with similar spectral characteristics are known as Riesz operators. Many classes of Riesz operators (including the compact operators) are ideals in
Holomorphic functional calculus
Holomorphic_functional_calculus
Polynomial Matrix Spectral Factorization or Matrix Fejer–Riesz Theorem is a tool used to study the matrix decomposition of polynomial matrices. Polynomial
Polynomial matrix spectral factorization
Polynomial_matrix_spectral_factorization
Physics theorem of interacting particles
electrostatics and Riesz potentials extensively studied in potential theory. Other classes of potentials, which not necessarily involve the Riesz kernel, for
Poppy-seed_bagel_theorem
Infinite series that is not convergent
Press. "Riesz summation method", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Werner Balser: "From Divergent Power Series to Analytic Functions", Springer-Verlag
Divergent_series
Method for assigning values to integrals
centered at the origin vanishes. This is the case, for instance, with the Riesz transforms. Consider the values of two limits: lim a → 0 + ( ∫ − 1 − a d
Cauchy_principal_value
C*-algebra
dimension group of an AF algebra is a Riesz group. The Effros-Handelman-Shen theorem says the converse is true. Every Riesz group, with a given scale, arises
Approximately finite-dimensional C*-algebra
Approximately_finite-dimensional_C*-algebra
Construction for adding objects to a Hilbert space
referred to as a pivot space. Note that even though Φ is isomorphic to Φ* (via Riesz representation) if it happens that Φ is a Hilbert space in its own right
Rigged_Hilbert_space
Generalized notion of measure in mathematics
real-valued functions on X, by the Riesz–Markov–Kakutani representation theorem. Angular displacement Complex measure Spectral measure Vector measure Riesz–Markov–Kakutani
Signed_measure
Decomposition of periodic functions
on R {\displaystyle \mathbb {R} } , given by F. Riesz. That is, if F {\displaystyle F} is a function of bounded variation on the interval [ 0 , P ] {\displaystyle
Fourier_series
Green's function for Laplacian
the Laplace equation. Double layer potential Green's function Riesz potential Green's function for the three-variable Laplace equation Evans, L.C. (1998)
Newtonian_potential
Bound on the norm of Fourier coefficients
theorem, found in 1910, in combination with the Riesz-Thorin theorem, originally discovered by Marcel Riesz in 1927. With this machinery, it readily admits
Hausdorff–Young_inequality
Concept in the solution of linear partial differential equations
dimensions. It was investigated for all dimensions for the Laplacian by Marcel Riesz. The existence of a fundamental solution for any operator with constant
Fundamental_solution
mathematics, the Riesz rearrangement inequality, sometimes called Riesz–Sobolev inequality, states that any three non-negative functions f : R n → R + {\displaystyle
Riesz rearrangement inequality
Riesz_rearrangement_inequality
Continuous maps on a closed subset of a normal space can be extended
if R {\displaystyle \mathbb {R} } is replaced by a general locally solid Riesz space. Dugundji (1951) extends the theorem as follows: If X {\displaystyle
Tietze_extension_theorem
Conjugate transpose of an operator in infinite dimensions
Banach space case when one identifies a Hilbert space with its dual (via the Riesz representation theorem). Then it is only natural that we can also obtain
Hermitian_adjoint
Type of operator in Fourier analysis
2. The corresponding problem for Bochner–Riesz multipliers is only partially solved; see also Bochner–Riesz conjecture. Calderón–Zygmund lemma Marcinkiewicz
Multiplier_(Fourier_analysis)
_{z}:f\mapsto f(z)} is a continuous linear functional on L2,h(D). By the Riesz representation theorem, this functional can be represented as the inner
Bergman_kernel
Theorem in complex analysis
q}=1,} by considering the function f ( z ) = ∫ | g | p z | h | q ( 1 − z ) . {\displaystyle f(z)=\int |g|^{pz}|h|^{q(1-z)}.} Riesz–Thorin theorem Phragmén–Lindelöf
Hadamard_three-lines_theorem
Proof that every structure with certain properties is isomorphic to another structure
compact Hausdorff spaces. The Riesz representation theorem states that a Hilbert space, such as the square-integrable function space L2(X) on a manifold X
Representation_theorem
Mathematical term
the weak topology. Starting in the early 1900s, David Hilbert and Marcel Riesz made extensive use of weak convergence. The early pioneers of functional
Weak_topology
Group with a compatible partial order
ℓ-group). A Riesz group is an unperforated partially ordered group with a property slightly weaker than being a lattice-ordered group. Namely, a Riesz group
Partially_ordered_group
Process of calculating the causal factors that produced a set of observations
on reasonable Banach spaces such as the L 2 {\displaystyle L^{2}} . F. Riesz theory states that the set of singular values of such an operator contains
Inverse_problem
Property of artificial neural networks
Cybenko, use methods from functional analysis, including the Hahn-Banach and Riesz–Markov–Kakutani representation theorems. Cybenko first published the theorem
Universal approximation theorem
Universal_approximation_theorem
Signal analysis tool
basis functions and the Riesz transform to handle Genuine Two-Dimensional EMD. The following is the form of the Riesz transform. For a complex function f
Hilbert–Huang_transform
Method in mathematics
Riemann–Liouville integral are generalized to arbitrary dimensions by the Riesz potential. In fractional calculus, these formulae can be used to construct
Cauchy formula for repeated integration
Cauchy_formula_for_repeated_integration
RIESZ FUNCTION
RIESZ FUNCTION
Male
Egyptian
, an Egyptian functionary.
Biblical
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Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Male
Egyptian
, a great functionary.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : apparently a variant of Reed.Possibly an Americanized spelling of German Reetz or Rietz.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, the son of the functionary Heknofre.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, a high Egyptian functionary.
RIESZ FUNCTION
RIESZ FUNCTION
Boy/Male
Hindu
Victor, Eldest daughter or a Nakshatra
Girl/Female
Arabic, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Muslim, Sindhi, Telugu
Lustrous; Wealthy; Diamond
Boy/Male
Shakespearean
Hamlet, Prince of Denmark' A courtier. Osric.
Female
Egyptian
, a daughter of King Amenhotep I.
Male
Serbian
(Дарко) Serbian name derived from Slavic dar, DARKO means "gift."
Boy/Male
French, German, Scandinavian
Warrior
Boy/Male
British, English
From the Clay Brook
Boy/Male
Celtic
Marksman.
Male
Italian
Italian form of Latin Vincentius, VINCENTE means "conquering."
Boy/Male
Arabic, Muslim
Precautious
RIESZ FUNCTION
RIESZ FUNCTION
RIESZ FUNCTION
RIESZ FUNCTION
RIESZ FUNCTION
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
pl.
of Limitary
pl.
of Lectionary
pl.
of Lachrymatory
pl.
of Ostiary
pl.
of Reliquary
pl.
of Protonotary
pl.
of Stationary
pl.
of Masticatory
pl.
of Ossuary
pl.
of Bursary
pl.
of Sacramentary
pl.
of Responsory
pl.
of Reformatory
pl.
of Refrigeratory
a.
Destitute of function, or of an appropriate organ. Darwin.
pl.
of Manufactory
pl.
of Signatory
pl.
of Eyry
pl.
of Stillatory