國立高雄大學圖資館 |

Language: English

Back

Quaternionic de Branges spaces and c...

Alpay, Daniel.

Quaternionic de Branges spaces and characteristic operator function

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quaternionic de Branges spaces and characteristic operator functionby Daniel Alpay, Fabrizio Colombo, Irene Sabadini.
Author:	Alpay, Daniel.
other author:	Colombo, Fabrizio.
Published:	Cham :Springer International Publishing :2020.
Description:	x, 116 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Functions, Quaternion.
Online resource:	https://doi.org/10.1007/978-3-030-38312-1
ISBN:	9783030383121$q(electronic bk.)

Quaternionic de Branges spaces and characteristic operator function
Alpay, Daniel.

Quaternionic de Branges spaces and characteristic operator function[electronic resource] /by Daniel Alpay, Fabrizio Colombo, Irene Sabadini. - Cham :Springer International Publishing :2020. - x, 116 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

Preliminaries -- 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.

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.

ISBN: 9783030383121$q(electronic bk.)

Standard No.: 10.1007/978-3-030-38312-1doiSubjects--Topical Terms:

678655
Functions, Quaternion.

LC Class. No.: QA196 / .A473 2020

Dewey Class. No.: 512.5

Quaternionic de Branges spaces and characteristic operator function
LDR:03051nmm a2200337 a 4500 001 573683
003 DE-He213
005 20200624150830.0
006 m d
007 cr nn 008maaau
008 200928s2020 sz s 0 eng d
020 $a 9783030383121$q(electronic bk.)
020 $a 9783030383114$q(paper)
024 7 $a 10.1007/978-3-030-38312-1 $2 doi
035 $a 978-3-030-38312-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA196 $b .A473 2020
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 512.5 $2 23
090 $a QA196 $b .A456 2020
100 1 $a Alpay, Daniel. $3 256504
245 1 0 $a Quaternionic de Branges spaces and characteristic operator function $h [electronic resource] / $c by Daniel Alpay, Fabrizio Colombo, Irene Sabadini.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a x, 116 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a Preliminaries -- 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.
520 $a 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.
650 0 $a Functions, Quaternion. $3 678655
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Functions of a Complex Variable. $3 275780
700 1 $a Colombo, Fabrizio. $3 511768
700 1 $a Sabadini, Irene. $3 308610
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u https://doi.org/10.1007/978-3-030-38312-1
950 $a Mathematics and Statistics (Springer-11649)