Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two

by Björn Gustafsson, Mihai Putinar

Overview

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.

Product Details

ISBN-13:	9783319658094
Publisher:	Springer International Publishing
Publication date:	10/29/2017
Series:	Lecture Notes in Mathematics , #2199
Edition description:	1st ed. 2017
Pages:	150
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

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.