Basic Analysis of Regularized Series and Products. 1st ed. 1993

種類:

電子ブック

責任表示:

by Jay Jorgenson, Serge Lang

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993

著者名:

• Jorgenson, Jay.
• Lang, Serge.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1564

ISBN:

9783540481935 [3540481931]    

注記:

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 analys

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