A Panorama of Hungarian Mathematics in the Twentieth Century, I

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Janos Horvath
Springer Science & Business Media, 28 de juny 2010 - 639 pàgines
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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 results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics.

The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.

 

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Continguts

PREFACE
7
TOPOLOGY
9
Constructive Function Theory
26
I ORTHOGONAL SERIES
29
ORTHOGONAL POLYNOMIALS
55
CLASSICAL UNWEIGHTED AND WEIGHTED INTERPOLATION
71
EXTREMAL PROPERTIES OF POLYNOMIALS
118
Harmonic Analysis
157
DIFFERENTIAL GEOMETRY
385
THE WORKS OF KORNEL LANCZOS ON THE THEORY OF RELATIVITY
414
DISCRETE AND CONVEX GEOMETRY
427
Stochastics
455
PROBABILITY THEORY
456
MATHEMATICAL STATISTICS
489
INFORMATION THEORY
523
CONTRIBUTION OF HUNGARIAN MATHEMATICIANS TO GAME THEORY
536

COMMUTATIVE HARMONIC ANALYSIS
159
NONCOMMUTATIVE HARMONIC ANALYSIS
193
A PANORAMA OF THE HUNGARIAN REAL AND FUNCTIONAL ANALYSIS IN THE 20TH CENTURY
211
HUNGARY THE EXTENDED FIRST HALF OF THE 20TH CENTURY
245
HOLOMORPHIC FUNCTIONS
295
THEODORE VON KARMAN
372
Geometry
383
A SHORT GUIDE TO THE HISTORY OF HUNGARY IN THE 20TH CENTURY
549
EDUCATION AND RESEARCH IN MATHEMATICS
555
BIOGRAPHIES
563
REFERENCES
608
NAME INDEX
623
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