Lecture Notes in Mathematics

Basic Analysis of Regularized Series and Products

Authors: Jorgenson, Jay, Lang, Serge

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About this book

Analytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis.

Table of contents (2 chapters)

Table of contents (2 chapters)
  • Some complex analytic properties of regularized products and series

    Pages 1-88

    Jorgenson, Jay A. (et al.)

  • A Parseval formula for functions with a singular asymptotic expansion at the origin

    Pages 89-117

    Jorgenson, Jay A. (et al.)

Buy this book

eBook $29.99
price for USA in USD
  • ISBN 978-3-540-48193-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Basic Analysis of Regularized Series and Products
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1564
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48193-5
DOI
10.1007/BFb0077194
Softcover ISBN
978-3-540-57488-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 130
Topics