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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Basic Analysis of Regularized Series and Products (Paperback, 1993 ed.)
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Basic Analysis of Regularized Series and Products (Paperback, 1993 ed.)
Series: Lecture Notes in Mathematics, 1564
Expected to ship within 18 - 22 working days
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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.
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