Gustafsson, Björn.
Hyponormal Quantization of Planar Domains Exponential Transform in Dimension Two / [electronic resource] : by Björn Gustafsson, Mihai Putinar. - 1st ed. 2017. - X, 150 p. 16 illus. in color. online resource. - Lecture Notes in Mathematics, 2199 0075-8434 ; . - Lecture Notes in Mathematics, 2199 .
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.
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.
9783319658100
10.1007/978-3-319-65810-0 doi
Functions of complex variables.
Operator theory.
Potential theory (Mathematics).
Numerical analysis.
Functions of a Complex Variable.
Operator Theory.
Potential Theory.
Numerical Analysis.
QA331-355
515.9
Hyponormal Quantization of Planar Domains Exponential Transform in Dimension Two / [electronic resource] : by Björn Gustafsson, Mihai Putinar. - 1st ed. 2017. - X, 150 p. 16 illus. in color. online resource. - Lecture Notes in Mathematics, 2199 0075-8434 ; . - Lecture Notes in Mathematics, 2199 .
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.
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.
9783319658100
10.1007/978-3-319-65810-0 doi
Functions of complex variables.
Operator theory.
Potential theory (Mathematics).
Numerical analysis.
Functions of a Complex Variable.
Operator Theory.
Potential Theory.
Numerical Analysis.
QA331-355
515.9