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This is a new annotated edition of Thomas J. Stieltjes' Collected
Papers, first published in 1914 (Vol. I) and 1918 (Vol. II) by
Noordhoff, Groningen, in French, and now published by
Springer-Verlag, originally to mark the occasion of the 100th
anniversary of Stieltjes' death (1894). These two volumes will be
of great interest to all mathematicians who are anxious to
understand the impact of Stieltjes' work on modern mathematics, and
in particular on the theory of orthogonal polynomials and continued
fractions. In addition to the reproduction of Stieltjes' papers
(I-XLVII), Volume I includes about 75 pages of commentaries by
contemporary mathematicians on Stieltjes' work. Volume II contains
Stieltjes' papers XLVIII-LXXXIV together with English translations
of his main paper "Recherches sur les fractions continues" and his
short note regarding the Riemann hypothesis. A Bibliography of
Stieltjes' papers is included in both volumes for the convenience
of the reader.
This is a new annotated edition of Thomas J. Stieltjes' Collected
Papers, first published in 1914 (Vol. I) and 1918 (Vol. II) by
Noordhoff, Groningen, in French, and now published by
Springer-Verlag, originally to mark the occasion of the 100th
anniversary of Stieltjes' death (1894). These two volumes will be
of great interest to all mathematicians who are anxious to
understand the impact of Stieltjes' work on modern mathematics, and
in particular on the theory of orthogonal polynomials and continued
fractions. In addition to the reproduction of Stieltjes' papers
(I-XLVII), Volume I includes about 75 pages of commentaries by
contemporary mathematicians on Stieltjes' work. Volume II contains
Stieltjes' papers XLVIII-LXXXIV together with English translations
of his main paper "Recherches sur les fractions continues" and his
short note regarding the Riemann hypothesis. A Bibliography of
Stieltjes' papers is included in both volumes for the convenience
of the reader.
This book is intended as an introduction to harmonic analysis and
generalized Gelfand pairs. Starting with the elementary theory of
Fourier series and Fourier integrals, the author proceeds to
abstract harmonic analysis on locally compact abelian groups and
Gelfand pairs. Finally a more advanced theory of generalized
Gelfand pairs is developed. This book is aimed at advanced
undergraduates or beginning graduate students. The scope of the
book is limited, with the aim of enabling students to reach a level
suitable for starting PhD research. The main prerequisites for the
book are elementary real, complex and functional analysis. In the
later chapters, familiarity with some more advanced functional
analysis is assumed, in particular with the spectral theory of
(unbounded) self-adjoint operators on a Hilbert space. From the
contents Fourier series Fourier integrals Locally compact groups
Haar measures Harmonic analysis on locally compact abelian groups
Theory and examples of Gelfand pairs Theory and examples of
generalized Gelfand pairs
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