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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Quaternionic de Branges Spaces and Characteristic Operator Function
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Quaternionic de Branges Spaces and Characteristic Operator Function
Daniel Alpay (Taschenbuch, Englisch)
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Beschreibung
This 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
28.01.2020
Sprache
Englisch
EAN
9783030383114
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
SpringerBriefs in Mathematics
Sonderedition
Nein
Autor
Daniel Alpay
Seitenanzahl
116
Auflage
1st edition 2020
Einbandart
Taschenbuch
Schlagwörter
quaternionic analysis, de Branges Rovnyak spaces, characteristic operator functions, quaternionic linear operators, S- spectrum, S-resolvent
Thema-Inhalt
PBKF - Funktionalanalysis und Abwandlungen
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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