LEADER 03917nam 22006735 450 001 9910257379203321 005 20210112211537.0 010 $a3-319-65810-7 024 7 $a10.1007/978-3-319-65810-0 035 $a(CKB)4100000000587420 035 $a(DE-He213)978-3-319-65810-0 035 $a(MiAaPQ)EBC6301081 035 $a(MiAaPQ)EBC5592370 035 $a(Au-PeEL)EBL5592370 035 $a(OCoLC)1021279346 035 $a(PPN)204533295 035 $a(EXLCZ)994100000000587420 100 $a20170930d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHyponormal Quantization of Planar Domains$b[electronic resource] $eExponential Transform in Dimension Two /$fby Björn Gustafsson, Mihai Putinar 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (X, 150 p. 16 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2199 311 $a3-319-65809-3 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThis book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2199 606 $aFunctions of complex variables 606 $aOperator theory 606 $aPotential theory (Mathematics) 606 $aNumerical analysis 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aFunctions of complex variables. 615 0$aOperator theory. 615 0$aPotential theory (Mathematics). 615 0$aNumerical analysis. 615 14$aFunctions of a Complex Variable. 615 24$aOperator Theory. 615 24$aPotential Theory. 615 24$aNumerical Analysis. 676 $a515.7246 700 $aGustafsson$b Björn$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721273 702 $aPutinar$b Mihai$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910257379203321 996 $aHyponormal Quantization of Planar Domains$92039123 997 $aUNINA