Vector and Operator Valued Measures and Applications
Vector and Operator Valued Measures and Applications

Author: Don H. Tucker

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 475

ISBN-13: 1483261026

DOWNLOAD EBOOK

Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.

Vector Measures
Vector Measures

Author: Joseph Diestel

Publisher: American Mathematical Soc.

Published: 1977-06-01

Total Pages: 338

ISBN-13: 0821815156

DOWNLOAD EBOOK

In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.

Operator-Valued Measures and Integrals for Cone-Valued Functions
Operator-Valued Measures and Integrals for Cone-Valued Functions

Author: Walter Roth

Publisher: Springer Science & Business Media

Published: 2009-02-05

Total Pages: 370

ISBN-13: 3540875646

DOWNLOAD EBOOK

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.

The Bartle-Dunford-Schwartz Integral
The Bartle-Dunford-Schwartz Integral

Author: Thiruvaiyaru V. Panchapagesan

Publisher: Springer Science & Business Media

Published: 2008-08-17

Total Pages: 311

ISBN-13: 3764386029

DOWNLOAD EBOOK

This volume is a thorough and comprehensive treatise on vector measures, treating the vectorial Radon integration in detail. It explores an interplay between, on the one side, linear operators, transferring real (complex) functions onto elements of locally convex Hausdorff spaces, and vector-valued measures, on the other. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature.

Stochastic Processes and Functional Analysis
Stochastic Processes and Functional Analysis

Author: Jerome Goldstein

Publisher: CRC Press

Published: 2020-09-24

Total Pages: 296

ISBN-13: 1000105423

DOWNLOAD EBOOK

"Covers the areas of modern analysis and probability theory. Presents a collection of papers given at the Festschrift held in honor of the 65 birthday of M. M. Rao, whose prolific published research includes the well-received Marcel Dekker, Inc. books Theory of Orlicz Spaces and Conditional Measures and Applications. Features previously unpublished research articles by a host of internationally recognized scholars."

Vector Measures, Integration and Related Topics
Vector Measures, Integration and Related Topics

Author: Guillermo Curbera

Publisher: Springer Science & Business Media

Published: 2010-02-21

Total Pages: 382

ISBN-13: 3034602111

DOWNLOAD EBOOK

This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.

Handbook of Measure Theory
Handbook of Measure Theory

Author: E. Pap

Publisher: Elsevier

Published: 2002-10-31

Total Pages: 1633

ISBN-13: 0080533094

DOWNLOAD EBOOK

The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.

Stochastic Processes: Theory and Methods
Stochastic Processes: Theory and Methods

Author: D N Shanbhag

Publisher: Gulf Professional Publishing

Published: 2001

Total Pages: 990

ISBN-13: 9780444500144

DOWNLOAD EBOOK

This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.

Stochastic Processes - Inference Theory
Stochastic Processes - Inference Theory

Author: Malempati M. Rao

Publisher: Springer

Published: 2014-11-14

Total Pages: 685

ISBN-13: 3319121723

DOWNLOAD EBOOK

This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.