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in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex manifold or
Holomorphic_separability
Complex-differentiable (mathematical) function
Biholomorphy Cauchy's estimate Harmonic maps Harmonic morphisms Holomorphic separability Meromorphic function Quadrature domains Wirtinger derivatives "Analytic
Holomorphic_function
Type of vector space in math
separable Hilbert spaces are therefore isometrically isomorphic to the square-summable sequence space, ℓ 2 . {\displaystyle \ell ^{2}.} Separability was
Hilbert_space
Type of mathematical functions
complex analysis of functions of one variable the functions studied are holomorphic or complex analytic so that, locally, they are power series in the variables
Function of several complex variables
Function_of_several_complex_variables
Study of complex manifolds and several complex variables
varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of
Complex_geometry
Relation among continuous functions
compact space is continuous. If, in addition, fn are holomorphic, then the limit is also holomorphic. The uniform boundedness principle states that a pointwise
Equicontinuity
Term in mathematics
intrinsically it can be defined as a complex manifold admitting a proper holomorphic embedding into C n {\displaystyle \mathbb {C} ^{n}} for some n {\displaystyle
Stein_manifold
analytic continuation An analytic continuation of a holomorphic function is a unique holomorphic extension of the function (on a connected open subset
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Award of the American Mathematical Society
Szabó for: Holomorphic disks and topological invariants for closed three-manifolds. Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. Holomorphic disks and
Oswald Veblen Prize in Geometry
Oswald_Veblen_Prize_in_Geometry
Generalized function whose value is zero everywhere except at zero
holomorphic functions f in D that are continuous on the closure of D. As a result, the delta function δz is represented in this class of holomorphic functions
Dirac_delta_function
Locally convex topological vector space that is also a complete metric space
Fréchet space. Let H {\displaystyle H} be the space of entire (everywhere holomorphic) functions on the complex plane. Then the family of seminorms | f | n
Fréchet_space
Generalization of covers
in general (under some slightly stronger hypotheses, on flatness and separability). Generically, then, such a morphism resembles a covering space in the
Branched_covering
Uniform approximation theorem in mathematics
variables, the Oka–Weil theorem is a result about the uniform convergence of holomorphic functions on Stein spaces due to Kiyoshi Oka and André Weil. The Oka–Weil
Oka–Weil_theorem
L function is entire (holomorphic on the entire complex plane). automorphic form An automorphic form is a certain holomorphic function. Bézout's identity
Glossary_of_number_theory
of Y is connected. Zariski, Oscar (1951), Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields, Memoirs
Zariski's connectedness theorem
Zariski's_connectedness_theorem
Family of solutions to related differential equations
{\displaystyle Y_{-n}(x)=(-1)^{n}Y_{n}(x).} Both Jα(x) and Yα(x) are holomorphic functions of x on the complex plane cut along the negative real axis
Bessel_function
Mathematical function
Bring radical. Over the complex numbers, algebraic functions have local holomorphic branches away from finitely many branch points and poles, and are naturally
Algebraic_function
Metric on a complex projective space endowed with Hermitian form
_{ij}=2(n+1)g_{ij}.} The common notions of separability apply for the Fubini–Study metric. More precisely, the metric is separable on the natural product of projective
Fubini–Study_metric
Second-order partial differential equation
coordinates, a coordinate system under which Laplace's equation becomes R-separable Helmholtz equation, a generalization of Laplace's equation Spherical harmonic
Laplace's_equation
Normed vector space that is complete
algebra A ( D ) {\displaystyle A(\mathbf {D} )} consists of functions holomorphic in the open unit disk D ⊆ C {\displaystyle D\subseteq \mathbb {C} } and
Banach_space
equations. Hodge–Arakelov theory Holomorphic functional calculus a branch of functional calculus starting with holomorphic functions. Homological algebra
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Mathematical theorem
inversion formula easily follows. The Segal–Bargmann space is the space of holomorphic functions on Cn that are square-integrable with respect to a Gaussian
Stone–von_Neumann_theorem
On when a family of real, continuous functions has a uniformly convergent subsequence
proof given above can be generalized in a way that does not rely on the separability of the domain. On a compact Hausdorff space X, for instance, the equicontinuity
Arzelà–Ascoli_theorem
dimensional vector space over the field. 4. Zariski's main lemma on holomorphic functions says the n-th symbolic power of a prime ideal in a polynomial
Glossary of commutative algebra
Glossary_of_commutative_algebra
Every polynomial has a real or complex root
similar argument also gives a proof of the maximum modulus principle for holomorphic functions). Continuing from before the principle was invoked, if a :=
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Bounded operators with sub-unit norm
{f_{r}(z))=\sum _{n\geq 0}r^{n}a_{n}z^{n}}} is holomorphic on |z| < 1/r. In that case fr(T) is defined by the holomorphic functional calculus and f (T ) can be
Contraction_(operator_theory)
Type of continuous linear operator
holomorphic functions on Ω {\displaystyle \Omega } , with the topology of uniform convergence on compact subsets. Many Banach spaces of holomorphic functions
Compact_operator
Duality for locally compact abelian groups
extended harmonic analysis beyond countable settings, removing certain separability assumptions and anticipating the need for a general locally compact framework
Pontryagin_duality
Barrelled space where closed and bounded subsets are compact
classical complex analysis, Montel's theorem asserts that the space of holomorphic functions on an open connected subset of the complex numbers has this
Montel_space
Counterintuitive mathematical object
two well-behaved functions, in the sense of those two functions being holomorphic. The Karush–Kuhn–Tucker conditions are first-order necessary conditions
Pathological_(mathematics)
Infinite sum
\operatorname {Re} (s)>1} , but the zeta function can be extended to a holomorphic function defined on C ∖ { 1 } {\displaystyle \mathbb {C} \setminus \{1\}}
Series_(mathematics)
Construction in algebra
, P ( G ) {\displaystyle {\mathcal {P}}(G)} (of continuous, smooth, holomorphic, regular functions) on groups are Hopf algebras in the category (Ste
Hopf_algebra
Commutative ring with no zero divisors other than zero
the ring H ( U ) {\displaystyle {\mathcal {H}}(U)} consisting of all holomorphic functions is an integral domain. The same is true for rings of analytic
Integral_domain
Algebraic structure with addition, multiplication, and division
is a complex manifold X. In this case, one considers the algebra of holomorphic functions, i.e., complex-valued differentiable functions. Their ratios
Field_(mathematics)
Generating function in integrable systems
,g}} be a basis for the space H 1 ( X ) {\displaystyle H^{1}(X)} of holomorphic differentials satisfying the standard normalization conditions ∮ a i
Tau function (integrable systems)
Tau_function_(integrable_systems)
Function in algebra
) / ( z − p ) j {\displaystyle f(z)/(z-p)^{j}} can be extended to a holomorphic function at p {\displaystyle p} . This means: if ν ( f ) = j > 0 {\displaystyle
Valuation_(algebra)
{\displaystyle K_{M}\otimes L^{\otimes m}} constructed from a positive holomorphic line bundle L {\displaystyle L} on a compact complex manifold M {\displaystyle
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Bourgain proved that the space H ∞ {\displaystyle H^{\infty }} of bounded holomorphic functions on the disk is a Grothendieck space. Dunford–Pettis property
Grothendieck_space
Locally convex topological vector space
separable if and only if its continuous dual is separable. This follows from the fact that for every normed space Y , {\displaystyle Y,} separability
Reflexive_space
construction, on the Hilbert space H = ℓ {\displaystyle \ell } 2(F2), of a holomorphic family of uniformly bounded representations πz of F2 for |z| < 1; these
Uniformly bounded representation
Uniformly_bounded_representation
Set of coordinates where the coordinate hypersurfaces all meet at right angles
real coordinates x and y, where i represents the imaginary unit. Any holomorphic function w = f(z) with non-zero complex derivative will produce a conformal
Orthogonal_coordinates
In functional analysis, a Hilbert space
H} are the restrictions to R {\displaystyle \mathbb {R} } of entire holomorphic functions, by the Paley–Wiener theorem. From the Fourier inversion theorem
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Topological vector spaces
led to investigation of the idea of hyperfunction, in which spaces of holomorphic functions are used as test functions. A refined theory has been developed
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
Open convex self-dual cones
for ||a|| ≤ 1 and g in SU(1,1). Where defined it is injective. It is holomorphic on D. By the maximum modulus principle, to show that g maps D onto D
Symmetric_cone
theorem states: if x is an element of a unital Banach algebra and f is a holomorphic function in a neighborhood of the spectrum σ ( x ) {\displaystyle \sigma
Glossary of functional analysis
Glossary_of_functional_analysis
Vector space with a notion of nearness
still of interest in analysis. Examples of such spaces are spaces of holomorphic functions on an open domain, spaces of infinitely differentiable functions
Topological_vector_space
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
Surname or Lastname
German (Stallmann)
German (Stallmann) : variant of Staller.German : topographic name for someone who lived in a muddy place, from the dialect word stal.English : habitational name from Stalmine in Lancashire, named probably with Old English stæll ‘creek’, ‘pool’ + Old Norse mynni ‘mouth’.English : possibly an occupational name for a stockman, from Middle English stall ‘stall’ + man ‘man’, or a topographic name for someone who lived by some cattle stalls.
Girl/Female
English American
and Kayla, meaning: keeper of the keys; pure.
Boy/Male
Gaelic Greek
Defender of man.
Boy/Male
Indian, Punjabi, Sikh
Reputation
Girl/Female
Indian
Blessed with Love, Waterfall
Girl/Female
Indian
Moon.
Biblical
same as Mahaz
Male
English
Medieval English form of Latin Felix, FELYSE means "happy" or "lucky."
Girl/Female
Muslim
Excellence
Boy/Male
Arabic, Australian, Muslim
Believer and Faithful to Allah
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
HOLOMORPHIC SEPARABILITY
a.
Of, pertaining to, or characterized by, trimorphism; -- contrasted with monomorphic, dimorphic, and polymorphic.
a.
Having, or occurring in, several distinct forms; -- opposed to monomorphic.
a.
Alt. of Homomorphous
a.
Of or pertaining to zoomorphism.
a.
Polymorphous.
a.
Of or pertaining to allomorphism.
n.
Quality of being separable or divisible; divisibility; separableness.
a.
Having but a single form; retaining the same form throughout the various stages of development; of the same or of an essentially similar type of structure; -- opposed to dimorphic, trimorphic, and polymorphic.
n.
The quality or state of being partible; divisibility; separability; as, the partibility of an inherttance.
n.
One of the asexual polymorphic forms of white ants, or termites, in which the head and jaws are very large and strong. The soldiers serve to defend the nest. See Termite.
a.
Alt. of Monomorphous