LEADER 03338nam 2200649 450 001 996466377003316 005 20230516165901.0 010 $a3-540-48193-1 024 7 $a10.1007/BFb0077194 035 $a(CKB)1000000000437165 035 $a(SSID)ssj0000321579 035 $a(PQKBManifestationID)12041903 035 $a(PQKBTitleCode)TC0000321579 035 $a(PQKBWorkID)10279765 035 $a(PQKB)10365162 035 $a(DE-He213)978-3-540-48193-5 035 $a(MiAaPQ)EBC5610923 035 $a(MiAaPQ)EBC6523260 035 $a(Au-PeEL)EBL5610923 035 $a(OCoLC)1079007314 035 $a(Au-PeEL)EBL6523260 035 $a(OCoLC)1120853422 035 $a(PPN)155204904 035 $a(EXLCZ)991000000000437165 100 $a20211012d1993 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBasic analysis of regularized series and products /$fJay Jorgenson, Serge Lang 205 $a1st ed. 1993. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1993] 210 4$dİ1993 215 $a1 online resource (X, 130 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1564 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-57488-3 320 $aIncludes bibliographical references (pages [119]-122). 330 $aAnalytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1564 606 $aSpectral theory (Mathematics) 606 $aSequences (Mathematics) 606 $aNumber theory 615 0$aSpectral theory (Mathematics) 615 0$aSequences (Mathematics) 615 0$aNumber theory. 676 $a512/.73 700 $aJorgenson$b Jay$060132 702 $aLang$b Serge$f1927-2005, 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466377003316 996 $aBasic analysis of regularized series and products$9382897 997 $aUNISA