Hyponormal Quantization of Planar Domains : Exponential Transform in Dimension Two

Mihai Putinar

ISBN 10: 3319658093 / ISBN 13: 9783319658094

Editore: Springer International Publishing, Springer International Publishing, 2017

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783319658094

Dati bibliografici

• Titolo: Hyponormal Quantization of Planar Domains : Exponential Transform in Dimension Two
• Editore: Springer International Publishing, Springer International Publishing
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3319658093
• ISBN 13: 9783319658094
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 9 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 9 millimetri di profondità
• Peso: 254 grammi

Descrizione articolo

Riassunto

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

Dalla quarta di copertina

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.