| Description |
1 online resource (639 pages) : illustrations |
| Series |
Bolyai Society mathematical studies ; 14 |
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Bolyai Society mathematical studies ; 14.
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| 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 |
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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 |
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8. GETTING CONVERGENCE BY RAISING THE DEGREE9. 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 |
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1. HAAR, VON NEUMANN, AND WIGNER1.1. 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 |
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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 |
| 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 broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable res |
| Bibliography |
Includes bibliographical references (pages 609-622) and index |
| Notes |
Print version record |
| Subject |
Mathematics -- Hungary
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Mathematicians -- Hungary -- Biography
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Matemáticos -- Hungría -- Biografías
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Mathematicians
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Mathematics
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Hungary
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| Genre/Form |
Biographies
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Biographies.
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Biographies.
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| Form |
Electronic book
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| Author |
Horváth, János
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| ISBN |
9783540307211 |
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3540307214 |
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1283250756 |
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9781283250757 |
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