Exponential Transform in Dimension Two Gustafsson, Björn. creator author. aut http://id.loc.gov/vocabulary/relators/aut Putinar, Mihai. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text gw 2017 1st ed. 2017. monographic eng

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electronic resource

access X, 150 p. 16 illus. in color. online resource. 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. 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. by Björn Gustafsson, Mihai Putinar. 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/ 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 9783319658100 https://doi.org/10.1007/978-3-319-65810-0 https://doi.org/10.1007/978-3-319-65810-0 Available to subscribing member institutions only. Доступно лише організаціям членам підписки. 170930 20210118121756.0 978-3-319-65810-0