04193nam a22006255i 4500 978-3-319-65810-0 DE-He213 20210118121756.0 cr nn 008mamaa 170930s2017 gw | s |||| 0|eng d 9783319658100 978-3-319-65810-0 10.1007/978-3-319-65810-0 doi QA331-355 PBKD bicssc MAT034000 bisacsh PBKD thema 515.9 23 Gustafsson, Björn. author. aut http://id.loc.gov/vocabulary/relators/aut Hyponormal Quantization of Planar Domains [electronic resource] : Exponential Transform in Dimension Two / by Björn Gustafsson, Mihai Putinar. 1st ed. 2017. Cham : Springer International Publishing : Imprint: Springer, 2017. X, 150 p. 16 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 0075-8434 ; 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. Functions of complex variables. Operator theory. Potential theory (Mathematics). Numerical analysis. Functions of a Complex Variable. http://scigraph.springernature.com/things/product-market-codes/M12074 Operator Theory. http://scigraph.springernature.com/things/product-market-codes/M12139 Potential Theory. http://scigraph.springernature.com/things/product-market-codes/M12163 Numerical Analysis. http://scigraph.springernature.com/things/product-market-codes/M14050 Putinar, Mihai. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) Springer eBooks Printed edition: 9783319658094 Printed edition: 9783319658117 Lecture Notes in Mathematics, 0075-8434 ; 2199 https://doi.org/10.1007/978-3-319-65810-0 ZDB-2-SMA ZDB-2-LNM 445319 445319 EB Available to subscribing member institutions only. Доступно лише організаціям членам підписки. Online access from local network of NaUOA. Online access with authorization at https://link.springer.com/ Онлайн-доступ з локальної мережі НаУОА. Онлайн доступ з авторизацією на https://link.springer.com/