Overview
- A self-contained exposition of the concept of "mother body" in potential theory
- Intriguing numerical experiments lacking theoretical explanation
- A new class of complex polynomials orthogonal with respect to a non Lebesgue space type norm
- Optimal storage and exact reconstruction of moments of a class of planar algebraic domains
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2199)
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Table of contents (8 chapters)
Keywords
About this book
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, approximationtheory, mathematical physics.
Authors and Affiliations
Bibliographic Information
Book Title: Hyponormal Quantization of Planar Domains
Book Subtitle: Exponential Transform in Dimension Two
Authors: Björn Gustafsson, Mihai Putinar
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-65810-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-65809-4Published: 30 September 2017
eBook ISBN: 978-3-319-65810-0Published: 29 September 2017
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 150
Number of Illustrations: 16 illustrations in colour
Topics: Functions of a Complex Variable, Operator Theory, Potential Theory, Numerical Analysis