Hyponormal Quantization of Planar Domains
Exponential Transform in Dimension Two
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Beschreibung
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.
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
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
Autor*in
Björn Gustafsson
Themen in »Hyponormal Quantization of Planar Domains«
momentum problem exponential transform orthogonal polynomial hyponormal operator rational approximation