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Polish-American mathematician (1900–1992)
Antoni Szczepan Zygmund (Polish pronunciation: [anˈtɔɲi ˈzɘgmunt]; 26 December 1900 – 30 May 1992) was a Polish-American mathematician. He worked mostly
Antoni_Zygmund
Name list
Zygmund is a given name and a surname, a cognate of Sigmund. Antoni Zygmund, Polish-American mathematician Zygmund Sazevich, American sculptor All pages
Zygmund
Mathematical theorem
In mathematics, the Marcinkiewicz–Zygmund inequality, named after Józef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection
Marcinkiewicz–Zygmund inequality
Marcinkiewicz–Zygmund_inequality
Probability equation in mathematics
In mathematics, the Paley–Zygmund inequality bounds the probability that a positive random variable is small, in terms of its first two moments. The inequality
Paley–Zygmund_inequality
Ruler of Poland–Lithuania (1587–1632), King of Sweden (1592–1599)
Sigismund III Vasa (Polish: Zygmunt III Waza, Lithuanian: Žygimantas Vaza; 20 June 1566 – 30 April 1632 N.S.) was King of Poland and Grand Duke of Lithuania
Sigismund_III_Vasa
Functions in harmonic analysis mathematics
^{n}\times \mathbb {R} ^{n}\to \mathbb {R} } is said to be a Calderón–Zygmund kernel if it satisfies the following conditions for some constants C >
Singular_integral
American sculptor (1899–1968)
Zygmund Sazevich (May 2, 1899, Kovno, Russia (now Kaunas, Lithuania) – 1968, San Francisco) was an American sculptor. He studied at the University of
Zygmund_Sazevich
Analysis theorem
In mathematics, the Calderón–Zygmund lemma is a fundamental result in Fourier analysis, harmonic analysis, and singular integrals. It is named for the
Calderón–Zygmund_lemma
Argentine-American mathematician
University of Chicago, where Calderón and his mentor, the analyst Antoni Zygmund, developed the theory of singular integral operators. This created the
Alberto_Calderón
Bound on probability of a random variable being far from its mean
densities. Several other related inequalities are also known. The Paley–Zygmund inequality gives a lower bound on tail probabilities, as opposed to Chebyshev's
Chebyshev's_inequality
American mathematician (1931–2018)
earned a Ph.D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching at MIT in 1955, moved to the University of Chicago in
Elias_M._Stein
United States Army officer (1894–1979)
Publishers, 1968. Zygmund, Dobbs. Red Intrigue and Race Turmoil. Foreword by Archibald B. Roosevelt. New York: The Alliance, Inc., 1954. Zygmund, Dobbs. The
Archibald_Roosevelt
Antoni Zygmund co-founded the school with his doctoral student Alberto Calderón at the University of Chicago in the 1950s. Over the years, Zygmund mentored
Chicago school (mathematical analysis)
Chicago_school_(mathematical_analysis)
Country in Central Europe
(with Alfred Tarski, Kazimierz Kuratowski, Wacław Sierpiński and Antoni Zygmund). Numerous mathematicians, scientists, chemists or economists emigrated
Poland
Polish mathematician (1890–1940)
Mathematics Genealogy Project Aleksander Rajchman from an article by Antoni Zygmund Zygmund, Antoni (1987), "Aleksander Rajchman (1890–1940)", Roczniki Polskiego
Aleksander_Rajchman
Mathematical inequality explaining concentration of random variables
In contrast to most commonly used concentration inequalities, the Paley-Zygmund inequality provides a lower bound on the deviation probability. The generic
Concentration_inequality
University in Warsaw, Poland
Sierpiński, Alfred Tarski, L. L. Zamenhof, Florian Znaniecki and Antoni Zygmund. In 1795, the partitions of Poland left Warsaw with access only to the
University_of_Warsaw
Lemma in mathematical analysis
maximal theorem. The lemma was a precursor in one dimension of the Calderón–Zygmund lemma. The lemma is stated as follows: Suppose g is a real-valued continuous
Rising_sun_lemma
Polish cyclist (1945–2021)
Zygmunt Hanusik (28 February 1945 – 4 March 2021) was a Polish cyclist. He competed in the individual road race at the 1968 Summer Olympics. Hanusik died
Zygmunt_Hanusik
Two-volume set of books by Antoni Zygmund
Antoni Zygmund wrote a classic two-volume set of books entitled Trigonometric Series, which discusses many different aspects of trigonometric series.
Trigonometric_Series
Name list
Europe Other names Alternative spelling Siegmund Nickname Sig Derived segaz "victory" + mundō "hand, protection" Related names Sigismund, Zygmund, Zygmunt
Sigmund_(given_name)
Mathematical concept
fundamental new techniques, introduced by Alberto Calderón and Antoni Zygmund in 1952, were developed by a number of authors to give general criteria
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
Fundamental trigonometric functions
(1970), p. 74. Powell (1981), p. 150. Rudin (1987), p. 88. Zygmund (1968), p. 1. Zygmund (1968), p. 11. Howie (2003), p. 24. Rudin (1987), p. 2. Brown
Sine_and_cosine
American soccer club
Galovic, Slavko Petrina, Tony Novacio, Tony Tadijanovic, Dusko Budimir, Zygmund Tryna. Founded 1949 Dissolved 1990 Stadium Hanson Stadium and Winnemac
Chicago_Croatian
Italian diplomat
Portugal, Habsburg Spain, the Queen of England, the Principality of Moldavia, Zygmund III Vasa and the Grand Vizier Sinan Pasha to whom he was related. He was
Bartolomeo_Bruti
Integral transform and linear operator
Hilbert transform. The Hilbert transform was a motivating example for Antoni Zygmund and Alberto Calderón during their study of singular integrals. Their investigations
Hilbert_transform
Polish mathematician (1910–1940)
multiplier theorem, Marcinkiewicz interpolation theorem, and Marcinkiewicz–Zygmund inequality. Following the outbreak of World War II, Marcinkiewicz enlisted
Józef_Marcinkiewicz
Theoretical framework in harmonic analysis
further by Polish mathematicians A. Zygmund and J. Marcinkiewicz in the 1930s using complex function theory (Zygmund 2002, chapters XIV, XV). E. M. Stein
Littlewood–Paley_theory
Private university in Chicago, Illinois, US
of Sociology". University of Chicago. Retrieved May 11, 2025. "Antoni Zygmund (1900-1992)". www-history.mcs.st-and.ac.uk. Retrieved September 9, 2026
University_of_Chicago
Mathematical study
one by one. The term is attributed to Polish mathematician Antoni Zygmund. Zygmund is said to have described the metaphor of the centipede thus: "You
Centipede_mathematics
Greek mathematician
research interests include Fourier analysis, singular integrals, and Calderón–Zygmund theory. He is well known for his contributions to the area of multilinear
Loukas_Grafakos
Area of mathematical analysis
interpolation arguments, and weighted norm inequalities. The theory of Calderón–Zygmund operators is one of the main developments in the analytic treatment of
Harmonic_analysis
Greek mathematician
constants in the theorems of M. Riesz, Zygmund and Kolmogorov written under the supervision of Antoni Zygmund. In 1972 Pichorides returned to Athens and
Stylianos_Pichorides
American mathematician (1934–2007)
and his Doctor of Philosophy degree in 1958, under supervision of Antoni Zygmund. The title of his doctoral thesis was Topics in the Theory of Uniqueness
Paul_Cohen
Mathematical problem in classical harmonic analysis
three. The original publishing dates are: Zygmund in 1935, Bari in 1961 and Katznelson in 1968. Zygmund's book was greatly expanded in its second publishing
Convergence_of_Fourier_series
American mathematician (1928–2021)
where he received in 1951 his master's degree and in 1956 under Antoni Zygmund his PhD with thesis On certain classes of function spaces and on the interpolation
Guido_Weiss
Function that is continuous everywhere but differentiable nowhere
Mathematics. 93 (1): 33–41. doi:10.2307/2373445. JSTOR 2373445. S2CID 124562827. Zygmund, A. (2002) [1935]. Trigonometric Series. Cambridge Mathematical Library
Weierstrass_function
Mathematical inequality relating inner products and norms
squares Minkowski inequality – Triangle inequality in Lp spaces Paley–Zygmund inequality – Probability equation in mathematics O'Connor, J.J.; Robertson
Cauchy–Schwarz_inequality
Representation of a type of random process
Burkholder–Davis–Gundy Doob's martingale Doob's upcrossing Kunita–Watanabe Marcinkiewicz–Zygmund Tools Cameron–Martin theorem Convergence of random variables Doléans-Dade
Autoregressive_model
Unincorporated community in Pennsylvania, US
Townships Abington, Cheltenham Commissioners Ann L. Rappoport (West) Mitchell Zygmund-Felt (Central) Brad M. Pransky (West) Area • Total 1.74 sq mi (4.51 km2)
Elkins_Park,_Pennsylvania
Discrete wavelets designed to have scaling functions with vanishing moments
{\displaystyle N/3-1} , and has been used in many applications using Calderón–Zygmund operators. Some theorems about Coiflets: For a wavelet system { ϕ , ϕ ~
Coiflet
Decomposition of periodic functions
of a distribution. "Fourier". Dictionary.com Unabridged (Online). n.d. Zygmund 2002, p. 1-8. Stillwell, John (2013). "Logic and the philosophy of mathematics
Fourier_series
Polish mathematician (1897–1942)
Antoni Zygmund, Analytic Functions, in 1933. It was translated into English in 1952 by E. J. Scott. In the preface to the English edition, Zygmund writes:
Stanisław_Saks
Awarded every year by the American Mathematical Society
significant work in homological algebra and its applications. 1979 Antoni Zygmund for his cumulative influence on the theory of Fourier series, real variables
Leroy_P._Steele_Prize
Sido S.1 and the M.N.5. The latter was designed by Józef Medwecki and Zygmund Nowakowski, both of whom worked for Samolot. With the company's help, two
Medwecki_and_Nowakowski_M.N.5
Fundamental theorem in probability theory and statistics
uniform distribution on the sphere c2 1 + ⋯ + c2 n = 1. Theorem (Salem–Zygmund)—Let U be a random variable distributed uniformly on (0,2π), and Xk = rk
Central_limit_theorem
Polish mathematician (1888–1945)
Borsuk, Bronisław Knaster, Kazimierz Kuratowski, Stanisław Saks, and Antoni Zygmund. For a time Mazurkiewicz was a professor at the University of Paris; however
Stefan_Mazurkiewicz
English mathematician
Littlewood: his 26 papers, written mostly in collaboration with Littlewood, Zygmund, Wiener and Ursell, opened new areas in analysis. — ‹See TfM›Béla Bollobás
Raymond_Paley
Branch of mathematics
Fourier analysis, but also other decomposition methods such as Calderón–Zygmund decompositions which break functions into parts that can be handled by
Mathematical_analysis
Georgian prince
Nowina 12. Dymitr Złotnicki h. Nowina 25. Elisaveta Dimitrievna Norova 6. Zygmund Czesław Złotnicki h. Nowina 26. Celestin Melchiorovich Treciak h. Sas 13
Irakli_Bagration_of_Mukhrani
Result in Fourier analysis
E (1939), The Theory of Functions (2nd ed.), Oxford University Press. Zygmund, Antoni (1968), Trigonometric Series (2nd ed.), Cambridge University Press
Parseval's_identity
Mathematical theory by discovered by Józef Marcinkiewicz
showed this result to Antoni Zygmund shortly before he died in World War II. The theorem was almost forgotten by Zygmund, and was absent from his original
Marcinkiewicz interpolation theorem
Marcinkiewicz_interpolation_theorem
Research collective
Fourier analysis has been advanced at Warsaw by: Aleksander Rajchman Antoni Zygmund Józef Marcinkiewicz Otton M. Nikodym Jerzy Spława-Neyman Polish School
Warsaw_School_(mathematics)
Type of function
space Karhunen–Loève theorem Lauricella's theorem Wannier function Antoni Zygmund (1935) Trigonometrical Series, page 6, Mathematical Seminar, University
Orthogonal_functions
Canadian mathematician
2 {\displaystyle \mathbb {R} ^{2}} and the Maximal Conjugated Calderon–Zygmund Operator, was supervised by F. Michael Christ. After short-term positions
Malabika_Pramanik
French mathematician
doctorate (Thèse d'État) with thesis Noyau de Cauchy et opérateurs de Caldéron-Zygmund supervised by Yves Meyer. David was from 1982 to 1989 an attaché de recherches
Guy_David_(mathematician)
Village in Khmelnytskyi, Ukraine
Zinkiv Castle on Zygmund Gerstmann's 1863 map
Zinkiv,_Khmelnytskyi_Oblast
Concept in probability theory
3 {\displaystyle \Pr(X\geq 3n/4)\leq {\frac {n/2}{3n/4}}=2/3} . Paley–Zygmund inequality – a corresponding lower bound Concentration inequality – a summary
Markov's_inequality
Mathematical theorem in real analysis
found in Benedetto & Czaja (2009), Stein & Shakarchi (2005), Wheeden & Zygmund (1977) and Rudin (1987). Since the statement is local in character, f can
Lebesgue differentiation theorem
Lebesgue_differentiation_theorem
Grand Duchess Leonida Georgievna of Russia
Georgievna, Grand Duchess of Russia 12. Dymitr Złotnicki h. Nowina 6. Zygmund Czesław Złotnicki h. Nowina 13. Celestyna Trzeciak h. Sas 3. Helena Złotnicka
Leonida_Bagration_of_Mukhrani
Mathematical operator in real and harmonic analysis
Cp,d are unknown. However subsequently Elias M. Stein used the Calderón-Zygmund method of rotations to prove the following: Theorem (Dimension Independence)
Hardy–Littlewood maximal function
Hardy–Littlewood_maximal_function
Calendar year
Oweini, 18th prime minister of Lebanon (d. 1971) December 25 – Antoni Zygmund, Polish mathematician (d. 1992) Rubén Jaramillo, Mexican peasant leader
1900
Modified summation method applicable to some divergent series
[1994], "Cesàro summation methods", Encyclopedia of Mathematics, EMS Press Zygmund, Antoni (1988) [1968], Trigonometric Series (2nd ed.), Cambridge University
Cesàro_summation
Type of singular integral operator
harmonic analysis. In particular, they arise in the proof of the Calderón-Zygmund inequality (Gilbarg & Trudinger 1983, §9.4). The Riesz transforms are given
Riesz_transform
Argentine mathematician
parabolic singular integrals, written under Alberto Pedro Calderón and Antoni Zygmund. Together with Mischa Cotlar, Sadosky wrote more than 30 articles as part
Cora_Sadosky
Wikidata Q455 https://celebratio.org/Zygmund_A/article/403/ https://history-of-approximation-theory.com/fpapers/zygmund_work.pdf BnF 12280001s O'Connor, John
List_of_Polish_mathematicians
American mathematician and philosopher (1894–1964)
He was interested in placing scholars such as Yuk-Wing Lee and Antoni Zygmund who had lost their positions. In 1941, Wiener accepted an appointment with
Norbert_Wiener
Equation in Fourier analysis
to Fourier Analysis and Wavelets., Brooks Cole, ISBN 978-0-534-37660-4 Zygmund, Antoni (1968), Trigonometric Series (2nd ed.), Cambridge University Press
Poisson_summation_formula
Spanish mathematician
Scientific Studies. Tolsa does research on harmonic analysis (Calderón-Zygmund theory), complex analysis, geometric measure theory, and potential theory
Xavier_Tolsa
with respect to dθ. The original statements are rather different (see Zygmund, Trigonometric Series, VII.8). The formulation here is as in Walter Rudin
F._and_M._Riesz_theorem
Branch of mathematics that studies dynamical systems
fail to be equidominated in Lp. Finally, if f is assumed to be in the Zygmund class, that is |f| log+(|f|) is integrable, then the ergodic means are
Ergodic_theory
1966 result in mathematical analysis
partout". Fundamenta Mathematicae. 4: 324–328. doi:10.4064/fm-4-1-324-328. Zygmund, A. (2002) [1935]. Trigonometric Series. Vol. I, II. Cambridge Mathematical
Carleson's_theorem
Musical artist
Retrieved 2024-11-02. "Nobuto". NMC. Retrieved 2024-11-02. de Somogyi, Zygmund (2022-06-27). "Interview: Ben Nobuto | PRXLUDES". PRXLUDES | beyond genre
Ben_Nobuto
Graduate-level textbooks in mathematics
1950-12-21 404 978-0691079349 25 Contributions to Fourier Analysis. A. Zygmund, W. Transue, M. Morse, A. P. Calderon, S. Bochner| 1950-08-21 196 978-0691079301
Annals_of_Mathematics_Studies
Inequality on approximations of a function by algebraic or trigonometric polynomials
1 {\displaystyle k=1} this result was proved by Dunham Jackson. Antoni Zygmund proved the inequality in the case when k = 2 , ω 2 ( t , f ) ≤ c t , t
Jackson's_inequality
lemma was subsequently applied to prove generalizations of the Calderón–Zygmund decomposition. Roughly speaking, the lemma states that it is possible to
Whitney_covering_lemma
Solution to a stochastic differential equation
Burkholder–Davis–Gundy Doob's martingale Doob's upcrossing Kunita–Watanabe Marcinkiewicz–Zygmund Tools Cameron–Martin theorem Convergence of random variables Doléans-Dade
Diffusion_process
lemma Geronimus 1946. Akhiezer 1965, pp. 180–181. Edwards 1982, pp. 72–73. Zygmund 2002, p. 11. Katznelson 2004, p. 40. Schmüdgen 2017, p. 260. Schmüdgen
Trigonometric_moment_problem
in Mathematics from the University of Oregon with a thesis titled Fatou-Zygmund Properties on Groups as a student of Kenneth A. Ross. Dr. López died on
Jorge_M._López
Movement that emerged from and reacts to postmodernism
Sufjan Stevens. London: Bloomsbury Academic. ISBN 9798216365549. Somogyi, Zygmund De (16 December 2022). "Here's to the Dreamers: Jennifer Walshe, Robin
Metamodernism
Zarankiewicz Stanisław Zaremba Henryk Zygalski, Enigma-breaker Antoni Zygmund, Polish-American Kazimierz Żorawski Banach Borsuk Eilenberg Iwaniec Janiszewski
List_of_Polish_people
American mathematician
-L.; Semmes, S.: Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation. [Calderón-Zygmund operators, para-accretive functions and
Stephen_Semmes
Method in probability theory
of the previous theorem can be refined by means of the so-called Paley–Zygmund inequality. Suppose that Xn is a sequence of non-negative real-valued random
Second_moment_method
Set of points on a line segment with certain topological properties
York: Springer-Verlag. Example 29. ISBN 978-0-486-68735-3. MR 0507446. Zygmund, A. (1958). Trigonometric Series, Vols. I and II. Cambridge University
Cantor_set
Etemadi's inequality Chung–Erdős inequality Khintchine inequality Paley–Zygmund inequality Laws of large numbers Asymptotic equipartition property Typical
List_of_probability_topics
American mathematician
mathematicians including Paul Halmos, André Weil, Saunders Mac Lane, Antoni Zygmund, and Shiing-Shen Chern. He remained on the faculty at this university until
Marshall_H._Stone
Stochastic volatility model used in derivatives markets
Burkholder–Davis–Gundy Doob's martingale Doob's upcrossing Kunita–Watanabe Marcinkiewicz–Zygmund Tools Cameron–Martin theorem Convergence of random variables Doléans-Dade
SABR_volatility_model
American mathematician
States. Studying under the wing of well-known mathematicians such as Antoni Zygmund, Brenner Morley continued her work in the field as a contributor to the
Vivienne_Esta_Morley
Annual cycling race in Algeria
Derycke 1954– 1968 No race 1969 Sweden Gösta Pettersson 1970 (1) Poland Zygmund Hanusik 1970 (2) East Germany Axel Peschel 1971 Poland Zbigniew Krzeszowiec
Tour_d'Algérie
Infinite sum of sines and cosines
subscripts α in Sα . Denjoy–Luzin theorem Hardy & Rogosinski 1999, pp. 2, 4. Zygmund 1968, pp. 6–7. Edwards 1979, pp. 158–159. Edwards 1982, pp. 95–96. Kechris
Trigonometric_series
Lenglart's inequality Marcinkiewicz–Zygmund inequality Markov's inequality McDiarmid's inequality Paley–Zygmund inequality Pinsker's inequality Popoviciu's
List_of_inequalities
The imaginary part of that function then defines the conjugate series. Zygmund (1968) studied the delicate questions of convergence of this series, and
Conjugate_Fourier_series
Statistical model allowing for frequent zero values
Mathematics and Economics. 59: 325–336. doi:10.1016/j.insmatheco.2014.09.012. Zygmund, A. (2002). Trigonometric Series. Cambridge: Cambridge University Press
Zero-inflated_model
Metric space with double measurement
MEASURES". Journal of the Korean Mathematical Society. 35 (1). ISSN 0304-9914. Zygmund, A. (2002). Trigonometric Series. Vol. I, II. Cambridge Mathematical Library
Doubling_space
Maximum a posteriori estimation Marchenko–Pastur distribution Marcinkiewicz–Zygmund inequality Marcum Q-function Margin of error Marginal conditional stochastic
List_of_statistics_articles
American mathematician
theory of Orthogonal polynomials, Pollard solved a conjecture of Antoni Zygmund, establishing mean convergence of the partial sums in L p {\displaystyle
Harry_Pollard_(mathematician)
Italian mathematician
May 5, 2013. Mingione, Giuseppe (2010). "Nonlinear aspects of Calderón-Zygmund theory". Jahresbericht der Deutschen Mathematiker-Vereinigung. 112 (3):
Giuseppe_Mingione
H. Stone 1983—Herman Goldstine, Isadore Singer 1986—Peter Lax, Antoni Zygmund 1987—Raoul Bott, Michael Freedman 1988—Ralph E. Gomory, Joseph Keller 1989—Samuel
List of National Medal of Science laureates
List_of_National_Medal_of_Science_laureates
Marcinkiewicz–Zygmund inequality / mnt Markov's inequality / (1:R) McDiarmid's inequality Multidimensional Chebyshev's inequality Paley–Zygmund inequality /
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Theorem on operator interpolation
operators, such as the Hardy–Littlewood maximal operator and the Calderón–Zygmund operators, do not have good endpoint estimates. In the case of the Hilbert
Riesz–Thorin_theorem
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