Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis, Daniel Alpay; Maria Elena Luna-Elizarrar?s; Michae

Автор: Alpay
Название: Slice Hyperholomorphic Schur Analysis
ISBN: 3319425137 ISBN-13(EAN): 9783319425139
Издательство: Springer
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Описание: This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.

Автор: Luna-Elizarrarбs M. Elena
Название: Bicomplex Holomorphic Functions
ISBN: 3319248669 ISBN-13(EAN): 9783319248660
Издательство: Springer
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Описание:

Introduction.- 1.The Bicomplex Numbers.- 2.Algebraic Structures of the Set of Bicomplex Numbers.- 3.Geometry and Trigonometric Representations of Bicomplex.- 4.Lines and curves in BC.- 5.Limits and Continuity.- 6.Elementary Bicomplex Functions.- 7.Bicomplex Derivability and Differentiability.- 8.Some properties of bicomplex holomorphic functions.- 9.Second order complex and hyperbolic differential operators.- 10.Sequences and series of bicomplex functions.- 11.Integral formulas and theorems.- Bibliography.

Автор: Daniel Alpay; Bernd Kirstein
Название: Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes
ISBN: 3319103342 ISBN-13(EAN): 9783319103341
Издательство: Springer
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Описание: The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich`s research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.

Автор: Daniel Alpay; Bernd Kirstein
Название: Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes
ISBN: 3319376721 ISBN-13(EAN): 9783319376721
Издательство: Springer
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Цена: 13275.00 р.
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Описание: The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich`s research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.

Автор: Daniel Alpay; Aad Dijksma; James Rovnyak; Hendrik
Название: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces
ISBN: 3034898231 ISBN-13(EAN): 9783034898232
Издательство: Springer
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Описание: Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares.

Автор: Tiberiu Constantinescu
Название: Schur Parameters, Factorization and Dilation Problems
ISBN: 3034899106 ISBN-13(EAN): 9783034899109
Издательство: Springer
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Описание: The subject of this book is about the ubiquity of the Schur parameters, whose introduction goes back to a paper of I. Schur in 1917 concerning an interpolation problem of C. Caratheodory. What followed there appears to be a truly fascinating story which, however, should be told by a professional historian. Here we provide the reader with a simplified version, mostly related to the contents of the book. In the twenties, thf theory of orthogonal polynomials on the unit circle was developed by G. Szego and the formulae relating these polynomials involved num- bers (usually called Szego parameters) similar to the Schur parameters. Mean- while, R. Nevanlinna and G. Pick studied the theory of another interpolation problem, known since then as the Nevanlinna-Pick problem, and an algorithm similar to Schur's one was obtained by Nevanlinna. In 1957, Z. Nehari solved OO an L problem which contained both Caratheodory-Schur and Nevannlina-Pick problems as particular cases. Apparently unrelated work of H. Weyl, J. von Neu- mann and K. Friedericks concerning selfadjoint extensions of symmetric operators was connected to interpolation by M. A. Naimark and M. G Krein using some gen- eral dilation theoretic ideas. Classical moment problems, like the trigonometric moment and Hamburger moment problems, were also related to these topics and a comprehensive account of what can be called the classical period has appeared in the monograph of M. G. Krein and A. A. Nudelman, KN].

Автор: Thomas Lam; Luc Lapointe; Jennifer Morse; Anne Sch
Название: k-Schur Functions and Affine Schubert Calculus
ISBN: 149390681X ISBN-13(EAN): 9781493906819
Издательство: Springer
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Описание: 1. Introduction.- 2. Primer on k-Schur Functions.- 3. Stanley symmetric functions and Peterson algebras.- 4. Affine Schubert calculus.

Автор: Daniel Alpay; Bernd Kirstein
Название: Interpolation, Schur Functions and Moment Problems II
ISBN: 3034807422 ISBN-13(EAN): 9783034807425
Издательство: Springer
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Описание: The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk.