LEADER 04300nam 22006015 450 001 996418279603316 005 20211006151245.0 010 $a3-030-38312-1 024 7 $a10.1007/978-3-030-38312-1 035 $a(CKB)4100000010121993 035 $a(DE-He213)978-3-030-38312-1 035 $a(MiAaPQ)EBC6031647 035 $a(PPN)242846343 035 $a(EXLCZ)994100000010121993 100 $a20200127d2020 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuaternionic de Branges Spaces and Characteristic Operator Function$b[electronic resource] /$fby Daniel Alpay, Fabrizio Colombo, Irene Sabadini 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (X, 116 p. 1 illus.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 311 $a3-030-38311-3 320 $aIncludes bibliographical references and index. 327 $aPreliminaries -- Quaternions and matrices -- Slice hyperholomorphic functions -- Rational functions -- Operator models -- Structure theorems for H(A;B) spaces -- J-contractive functions -- The characteristic operator function -- L() spaces and linear fractional transformations -- Canonical differential systems. 330 $aThis work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aFunctional analysis 606 $aOperator theory 606 $aFunctions of complex variables 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aFunctions of complex variables. 615 14$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aFunctions of a Complex Variable. 676 $a512.5 700 $aAlpay$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$054298 702 $aColombo$b Fabrizio$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSabadini$b Irene$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418279603316 996 $aQuaternionic de Branges Spaces and Characteristic Operator Function$92547779 997 $aUNISA