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 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.

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

Dettagli sul prodotto

• Autori: Mihai Putinar, Björn Gustafsson
• Editore: Springer, Berlin
• Contenuto: Libro
• Forma del prodotto: Tascabile
• Data pubblicazione: 30.09.2017
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Analisi
• EAN: 9783319658094
• ISBN: 978-3-31-965809-4
• Numero di pagine: 150
• Illustrazioni: X, 150 p. 16 illus. in color.
• Dimensioni (della confezione): 15.6 x 23.4 x 0.8 cm
• Peso (della confezione): 268 g
• Serie: Lecture Notes in Mathematics > 2199
• Categorie: Analysis, B, Calculus, Analysis / Funktionalanalysis, Funktionalanalysis, Numerik (naturwissenschaftlich, EDV), Mathematische Analysis, allgemein, Funktionalanalysis und Abwandlungen, Numerische Mathematik, Mathematics and Statistics, Numerical analysis, Stochastics, Functional analysis & transforms, Operator Theory, Functions of a Complex Variable, Functions of complex variables, Potential Theory, Potential theory (Mathematics), Orthogonalpolynomial, hyponormaloperator, momentumproblem, RationalApproximation, exponentialtransform