Hyponormal quantization of planar domains : exponential transform in dimension two / Bjorn Gustafsson and Mihai Putinar.
By: Gustafsson, Bjorn [author].
Contributor(s): Putinar, Mihai [author].
Material type: TextSeries: Lecture notes in mathematics ; 2199.Publisher: Cham : Springer, 2017Description: x, 148 pages : illustrations (some color) ; 24 cm.ISBN: 9783319658094 (alk. paper).Subject(s): Operational CalculusDDC classification: 515.72Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

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515.72 F299 Algebraic structures and operator calculus  515.72 F487 Operator theory  515.72 G463 Operator functions and localization of spectra  515.72 G982 Hyponormal quantization of planar domains :  515.72 In61(86) Invariant subspaces and allied topics  515.72 J45 Spectral properties of noncommuting operators  515.72 K85 Operations research and discrete analysis 
Include index and bibliographical references.
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 rankone selfcommutators 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.
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