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000928554 0247_ $$a10.1007/978-3-030-38
000928554 0247_ $$a10.1007/978-3-030-38312-1$$2doi
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000928554 1001_ $$aAlpay, Daniel.
000928554 24510 $$aQuaternionic de Branges spaces and characteristic operator function /$$cDaniel Alpay, Fabrizio Colombo, Irene Sabadini.
000928554 260__ $$aCham :$$bSpringer,$$c2020.
000928554 300__ $$a1 online resource (121 pages).
000928554 336__ $$atext$$btxt$$2rdacontent
000928554 337__ $$acomputer$$bc$$2rdamedia
000928554 338__ $$aonline resource$$bcr$$2rdacarrier
000928554 347__ $$atext file$$bPDF$$2rda
000928554 4901_ $$aSpringerBriefs in Mathematics
000928554 504__ $$aIncludes bibliographical references and index.
000928554 5050_ $$aPreliminaries -- Quaternions and matrices -- Slice hyperholomorphic functions -- Rational functions -- Operator models -- Structure theorems for H(A;B) spaces -- J-contractive functions -- The characteristic operator function -- L() spaces and linear fractional transformations -- Canonical differential systems.
000928554 506__ $$aAccess limited to authorized users.
000928554 520__ $$aThis work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book.
000928554 588__ $$aDescription based on print version record.
000928554 650_0 $$aFunctions, Quaternion.
000928554 7001_ $$aColombo, Fabrizio.
000928554 7001_ $$aSabadini, Irene,$$d1965-
000928554 77608 $$iPrint version:$$aAlpay, Daniel$$tQuaternionic de Branges Spaces and Characteristic Operator Function$$dCham : Springer,c2020$$z9783030383114
000928554 830_0 $$aSpringerBriefs in mathematics.
000928554 852__ $$bebk
000928554 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-38312-1$$zOnline Access$$91397441.1
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000928554 983__ $$aOnline
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