03048nam a2200445 i 4500991003573749707536m o d cr |n|||||||||181120s2017 sz ob 001 0 eng d3319658107(electronic bk.)9783319658100(electronic bk.)10.1007/978-3-319-65810-0doib14353805-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.923LC QA331-355Gustafsson, Björn.721273Hyponormal Quantization of Planar Domains[e-book] :Exponential Transform in Dimension Two /by Björn Gustafsson, Mihai PutinarCham :Springer,20171 online resource (x, 150 p. 16 illus. in color.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture Notes in Mathematics,0075-8434 ;2199Includes bibliographical references and index1 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 ; ReferencesThis 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 physicsHilbert spaceHyponormal operatorsRiemann surfacesPutinar, Mihaiauthorhttp://id.loc.gov/vocabulary/relators/aut55885Springer eBooksPrinted edition:9783319658094https://link.springer.com/book/10.1007/978-3-319-65810-0An electronic book accessible through the World Wide.b1435380503-03-2220-11-18991003573749707536Hyponormal quantization of planar domains1522946UNISALENTOle01320-11-18m@ -engsz 00