LEADER 03048nam a2200445 i 4500 001 991003573749707536 006 m o d 007 cr |n||||||||| 008 181120s2017 sz ob 001 0 eng d 020 $a3319658107$q(electronic bk.) 020 $a9783319658100$q(electronic bk.) 024 7 $a10.1007/978-3-319-65810-0$2doi 035 $ab14353805-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.9$223 084 $aLC QA331-355 100 1 $aGustafsson, Bjo?rn.$0721273 245 10$aHyponormal Quantization of Planar Domains$h[e-book] :$bExponential Transform in Dimension Two /$cby Björn Gustafsson, Mihai Putinar 260 $aCham :$bSpringer,$c2017 300 $a1 online resource (x, 150 p. 16 illus. in color.) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 347 $atext file$bPDF$2rda 490 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2199 504 $aIncludes bibliographical references and index 505 0 $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 520 $aThis book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics 650 0$aHilbert space 650 0$aHyponormal operators 650 0$aRiemann surfaces 700 1 $aPutinar, Mihai$eauthor$4http://id.loc.gov/vocabulary/relators/aut$055885 773 0 $aSpringer eBooks 776 08$iPrinted edition:$z9783319658094 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-65810-0$zAn electronic book accessible through the World Wide 907 $a.b14353805$b03-03-22$c20-11-18 912 $a991003573749707536 996 $aHyponormal quantization of planar domains$91522946 997 $aUNISALENTO 998 $ale013$b20-11-18$cm$d@ $e-$feng$gsz $h0$i0