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Hyponormal quantization of planar domains: exponential transform in dimension two

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 o...

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Detalles Bibliográficos
Autores principales: Gustafsson, Björn, Putinar, Mihai
Lenguaje:eng
Publicado: Springer 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-65810-0
http://cds.cern.ch/record/2287937
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author Gustafsson, Björn
Putinar, Mihai
author_facet Gustafsson, Björn
Putinar, Mihai
author_sort Gustafsson, Björn
collection CERN
description 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.
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spelling cern-22879372021-04-21T19:02:59Zdoi:10.1007/978-3-319-65810-0http://cds.cern.ch/record/2287937engGustafsson, BjörnPutinar, MihaiHyponormal quantization of planar domains: exponential transform in dimension twoMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:22879372017
spellingShingle Mathematical Physics and Mathematics
Gustafsson, Björn
Putinar, Mihai
Hyponormal quantization of planar domains: exponential transform in dimension two
title Hyponormal quantization of planar domains: exponential transform in dimension two
title_full Hyponormal quantization of planar domains: exponential transform in dimension two
title_fullStr Hyponormal quantization of planar domains: exponential transform in dimension two
title_full_unstemmed Hyponormal quantization of planar domains: exponential transform in dimension two
title_short Hyponormal quantization of planar domains: exponential transform in dimension two
title_sort hyponormal quantization of planar domains: exponential transform in dimension two
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-65810-0
http://cds.cern.ch/record/2287937
work_keys_str_mv AT gustafssonbjorn hyponormalquantizationofplanardomainsexponentialtransformindimensiontwo
AT putinarmihai hyponormalquantizationofplanardomainsexponentialtransformindimensiontwo