Main Lectures on Gaussian Integral Operators and Classical Groups
Lectures on Gaussian Integral Operators and Classical Groups cover

Lectures on Gaussian Integral Operators and Classical Groups

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This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis. A publication of the European Mathematical [...]Society (EMS). Distributed within the Americas by the American Mathematical Society.
Request Code : ZLIB.IO17636971
Categories:
Year:
2022
Publisher:
EMS
Language:
English
ISBN 10:
3037190809
ISBN 13:
9783037190807
ISBN:
3037190809, 9783037190807
Series:
EMS Series of Lectures in Mathematics

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