Quaternionic de Branges Spaces and Characteristic Operator Function (SpringerBriefs in Mathematics)

Science & Math

Alpay, Daniel

Colombo, Fabrizio

Sabadini, Irene

Mathematics

Springer

Exercises in Applied Mathematics: With a View toward Information Theory, Machine Learning, Wavelets, and Statistical Physics (Chapman Mathematical Notes)

Computers & Technology

Computer Science

Birkhauser

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions (Operator Theory: Advances and Applications, 304)

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)

Rovnyak, James

Dijksma, Aad

Snoo, Hendrik de

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It defines the notion of bicomplex modules and then develops the theory of linear functionals and linear operators on bicomplex modules.

Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis (SpringerBriefs in Mathematics)

Struppa, Daniele C.

Shapiro, Michael

Luna-Elizarrarás, Maria Elena

Reference

This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration.
Benefits of the 2nd edition
Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

A Complex Analysis Problem Book

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.

Slice Hyperholomorphic Schur Analysis (Operator Theory: Advances and Applications, 256)

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.

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Birkhäuser Basel

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Books by Alpay, Daniel

See the best price to sell, buy, or rent books by Alpay, Daniel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Quaternionic de Branges Spaces and Characteristic Operator Function (SpringerBriefs in Mathematics)

Exercises in Applied Mathematics: With a View toward Information Theory, Machine Learning, Wavelets, and Statistical Physics (Chapman Mathematical Notes)

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions (Operator Theory: Advances and Applications, 304)

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)

Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis (SpringerBriefs in Mathematics)

An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

A Complex Analysis Problem Book

Slice Hyperholomorphic Schur Analysis (Operator Theory: Advances and Applications, 256)

Slice Hyperholomorphic Schur Analysis (Operator Theory: Advances and Applications, 256)

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)