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＜電子ブック＞
Basic Analysis of Regularized Series and Products / by Jay Jorgenson, Serge Lang
(Lecture Notes in Mathematics. ISSN:16179692 ; 1564)

版	1st ed. 1993.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1993
本文言語	英語
大きさ	X, 130 p : online resource
冊子体	Basic analysis of regularized series and products / Jay Jorgenson, Serge Lang ; : gw. pbk,: us. pbk
著者標目	*Jorgenson, Jay author Lang, Serge author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Mathematical analysis LCSH:Geometry, Differential FREE:Number Theory FREE:Analysis FREE:Differential Geometry
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/BFb0077194

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