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A panorama of Hungarian mathematics in the twentieth century I

Author: János Horváth
Publisher: Heidelberg : Springer-Verlag, ©2006.
Series: Bolyai Society mathematical studies, 14.
Edition/Format:   eBook : Document : Biography : EnglishView all editions and formats
Summary:
A glorious period of Hungarian mathematics started in 1900 when Lipót Fejér discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians  Read more...
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Genre/Form: Electronic books
Biography
Additional Physical Format: Print version:
Material Type: Biography, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: János Horváth
ISBN: 9783540307211 3540307214 1283250756 9781283250757
OCLC Number: 649394701
Description: 1 online resource (639 pages) : illustrations.
Contents: ""Cover ""; ""Title Page ""; ""Copyright Page ""; ""Table of Contents ""; ""PREFACE""; ""TOPOLOGY""; ""REFERENCES""; ""Constructive Function Theory ""; ""CONSTRUCTIVE FUNCTION THEORY: I. ORTHOGONAL SERIES ""; ""1. THE RIESZ-FISCHER THEOREM""; ""2. RIESZ TYPICAL MEANS""; ""3. THE HAAR ORTHOGONAL SYSTEM ""; ""4. THE SATURATION PROBLEM FOR THE FEJER MEANS ""; ""5. ALMOST EVERYWHERE CONVERGENCE OF ORTHOGONAL SERIES ""; ""6. CESARO SUMMABILITY OF ORTHOGONAL SERIES ""; ""7. UNCONDITIONAL CONVERGENCE OF ORTHOGONAL SERIES""; ""REFERENCES""; ""ORTHOGONAL POLYNOMIALS""; ""REFERENCES"" ""CLASSICAL (UNWEIGHTED) AND WEIGHTED INTERPOLATION """"1. INTRODUCTION""; ""A CLASSICAL CASE ""; ""2. LAGRANGE INTERPOLATION. LEBESGUE FUNCTION. LEBESGUE CONSTANT. OPTIMAL LEBESGUE CONSTANT. DIVERGENCE OF INTERPOLATION ""; ""3. ON THE CONVERGENCE OF THE INTERPOLATORY PROCESSES""; ""4. HERMITE-FEJER TYPE AND OTHER CONVERGENT INTERPOLATORY PROCESSES ""; ""5. LACUNARY OR BIRKHOFF INTERPOLATION""; ""6. ON THE MEAN CONVERGENCE OF INTERPOLATION""; ""B WEIGHTED CASE ""; ""7. WEIGHTED LAGRANGE INTERPOLATION , WEIGHTED LEBESGUE FUNCTION, WEIGHTED LEBESGUE CONSTANT "" ""8. GETTING CONVERGENCE BY RAISING THE DEGREE""""9. MEAN CONVERGENCE""; ""REFERENCES""; ""EXTREMAL PROPERTIES OF POLYNOMIALS""; ""1. MARKOV- AND BERNSTEIN-TYPE INEQUALITIES""; ""2. MUNTZ POLYNOMIALS AND EXPONENTIAL SUMS""; ""3. GEOMETRIC PROPERTIES OF POLYNOMIALS""; ""REFERENCES""; ""Harmonic Analysis""; ""COMMUTATIVE HARMONIC ANALYSIS""; ""1. THE THEOREM OF FEJER""; ""2. THE THEOREM OF RIESZ-FISCHER ""; ""3. BOUNDARY VALUES OF ANALYTIC FUNCTIONS""; ""4. RIESZ PRODUCT AND SIDON SETS""; ""5. MISCELLANEOUS*""; ""REFERENCES""; ""NON-COMMUTATIVE HARMONIC ANALYSIS"" ""1. HAAR, VON NEUMANN , AND WIGNER""""1.1. Hilbert's Fifth Problem""; ""1.2. Invariant Measures and Analysis on Locally Compact Groups""; ""1.3. Representation Theory and Quantum Physics""; ""1.4 . Invariant Means and Almost Periodic Functions and Groups""; ""1.5. Von Neumann Algebras""; ""1.6. Development of Unitary Representation Theory of Non-Compact Lie Groups ""; ""2. SZ.-NAGY AND PUKANSZKY""; ""2.1. Bela Sz.-Nagy""; ""2.2. Lajos Pukanszky""; ""REFERENCES""; ""A PANORAMA OF THE HUNGARIAN REAL AND FUNCTIONAL ANALYSIS IN THE 20TH CENTURY ""; ""REFERENCES"" ""DIFFERENTIAL EQUATIONS: HUNGARY, THE EXTENDED FIRST HALF OF THE 20TH CENTURY """"Introduction""; ""Summary.""; ""At the turn of the century.""; ""Lajos Schlesinger and his work.""; ""Fejer summation theorem and the Dirichlet problem on the unit disc. ""; ""The work of Fejer in mechanics and his habilitation lecture.""; ""F. Riesz' subharmonic functions.""; ""The works of F. Riesz and Haar on linear integral equations.""; ""Haar's inequality for partial equations of the first order.""; ""Haar's existence and uniqueness theorem in the calculus of variations.""; ""T. Rado's regularity Lemma.""
Series Title: Bolyai Society mathematical studies, 14.
Responsibility: János Horváth (Ed.).
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Abstract:

A glorious period of Hungarian mathematics started in 1900 when Lipot Fejer discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and  Read more...

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From the reviews:"This highly interesting book is more than a report on a glorious period of Hungarian mathematics. It is a survey of twentieth century mathematics describing the development of the Read more...

 
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