Introduction to the Theory of Linear Nonselfadjoint Operators
Author: Israel Gohberg
Publisher: American Mathematical Soc.
Published: 1978
Total Pages: 402
ISBN-13: 9780821886502
DOWNLOAD EBOOKPosts
Commuting Nonselfadjoint Operators in Hilbert Space
Author: Moshe S. Livsic
Publisher: Springer
Published: 2006-11-15
Total Pages: 116
ISBN-13: 3540478779
DOWNLOAD EBOOKClassification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves.
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
Author: Tailen Hsing
Publisher: John Wiley & Sons
Published: 2015-05-06
Total Pages: 363
ISBN-13: 0470016914
DOWNLOAD EBOOKTheoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
History of Banach Spaces and Linear Operators
Author: Albrecht Pietsch
Publisher: Springer Science & Business Media
Published: 2007-12-31
Total Pages: 877
ISBN-13: 0817645969
DOWNLOAD EBOOKWritten by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Introduction to Operator Space Theory
Author: Gilles Pisier
Publisher: Cambridge University Press
Published: 2003-08-25
Total Pages: 492
ISBN-13: 9780521811651
DOWNLOAD EBOOKAn introduction to the theory of operator spaces, emphasising applications to C*-algebras.
An Introduction to Hankel Operators
Author: Jonathan R. Partington
Publisher: Cambridge University Press
Published: 1988
Total Pages: 113
ISBN-13: 0521366119
DOWNLOAD EBOOKHankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Harmonic Analysis of Operators on Hilbert Space
Author: Béla Sz Nagy
Publisher: Springer Science & Business Media
Published: 2010-09-01
Total Pages: 481
ISBN-13: 1441960937
DOWNLOAD EBOOKThe existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Semidefinite Optimization and Convex Algebraic Geometry
Author: Grigoriy Blekherman
Publisher: SIAM
Published: 2012-01-01
Total Pages: 495
ISBN-13: 9781611972290
DOWNLOAD EBOOKThis book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This quickly evolving research area with contributions from the diverse fields of convex geometry, algebraic geometry, and optimization is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of convex algebraic geometry. The book begins with an introduction to nonnegative polynomials and sums of squares and their connections to semidefinite programming and quickly advances to several areas at the forefront of current research. These include (1) semidefinite representability of convex sets, (2) duality theory from the point of view of algebraic geometry, and (3) nontraditional topics such as sums of squares of complex forms and noncommutative sums of squares polynomials. Suitable for a class or seminar, with exercises aimed at teaching the topics to beginners, Semidefinite Optimization and Convex Algebraic Geometry serves as a point of entry into the subject for readers from multiple communities such as engineering, mathematics, and computer science. A guide to the necessary background material is available in the appendix.
C* - Algebras and Numerical Analysis
Author: Ronald Hagen
Publisher: CRC Press
Published: 2000-09-07
Total Pages: 388
ISBN-13: 9780824704605
DOWNLOAD EBOOK"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."
Proceedings of the St. Petersburg Mathematical Society
Author: N.N. Uraltseva (Mathematikerin, Russland)
Publisher: American Mathematical Soc.
Published:
Total Pages: 252
ISBN-13: 9780821896044
DOWNLOAD EBOOKThis collection presents new results in algebra, functional analysis, and mathematical physics. In particular, evolution and spectral problems related to small motions of viscoelastic fluid are considered. Specific areas covered in the book include functional equations and functional operator equations from the point of view of the $C*$-algebraic approach, the existence of an isomorphism between certain ideals regarded as Galois modules, spectral problems in singularly perturbed domains, scattering theory, the existence of bounded solutions to the equation $\operatorname{div} u = f$ in a plane domain, and a compactification of a locally compact group. Also given is an historic overview of the mathematical seminars held at St. Petersburg State University. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.
