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＜電子ブック＞
Hyponormal Quantization of Planar Domains : Exponential Transform in Dimension Two / by Björn Gustafsson, Mihai Putinar
(Lecture Notes in Mathematics. ISSN:16179692 ; 2199)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	X, 150 p. 16 illus. in color : online resource
著者標目	*Gustafsson, Björn author Putinar, Mihai author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Operator theory LCSH:Potential theory (Mathematics) LCSH:Numerical analysis FREE:Functions of a Complex Variable FREE:Operator Theory FREE:Potential Theory FREE:Numerical Analysis
一般注記	1 Introduction -- 2 The exponential transform -- 3 Hilbert space factorization -- 4 Exponential orthogonal polynomials -- 5 Finite central truncations of linear operators -- 6 Mother bodies -- 7 Examples -- 8 Comparison with classical function spaces -- A Hyponormal operators -- Glossary -- Index -- References This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory,mathematical physics HTTP:URL=https://doi.org/10.1007/978-3-319-65810-0

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