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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with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active.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.
Content Level »Research
Keywords »Analysis - Fourier series - Geometry - History of Mathematics - Hungarian Mathematics - Minimum - Stochastics - calculus - differential equation - extrema - functional analysis - operator theory - orthogonal polynomials - statistics
Topology.- Topology.- Constructive Function Theory.- Constructive Function Theory: I. Orthogonal Series.- Orthogonal Polynomials.- Classical (Unweighted) and Weighted Interpolation.- Extremal Properties of Polynomials.- Harmonic Analysis.- Commutative Harmonic Analysis.- Non-Commutative Harmonic Analysis.- A Panorama of the Hungarian Real and Functional Analysis in the 20Th Century.- Differential equations: Hungary, the extended first half of the 20Th century.- Holomorphic Functions.- Theodore von Kármán.- Geometry.- Differential geometry.- The Works of Kornél Lánczos on the Theory of Relativity.- Discrete and Convex Geometry.- Stochastics.- Probability theory.- Mathematical Statistics.- Stochastics: Information Theory.- Contribution of Hungarian Mathematicians to Game Theory.- A Short Guide to The History of Hungary in The 20th Century.- Education And Research In Mathematics.- Biographies.