Functional analysis and probability / Mark Burgin, editor.

Format:

Book

Contributor:

Burgin, M. S. (Mark Semenovich), editor.

Series:

Mathematics research developments series.

Mathematics Research Developments

Language:

English

Subjects (All):

Functional analysis.

Probabilities.

Physical Description:

1 online resource (478 p.)

Place of Publication:

New York, [New York] : Nova Publishers, 2015.

Language Note:

English

Summary:

The following topics are presented in the corresponding parts of this book: 1. Measure and Integration 2. Equations and Inequalities 3. Operators4. Probability5. Applications

Contents:

FUNCTIONAL ANALYSISAND PROBABILITY; FUNCTIONAL ANALYSISAND PROBABILITY; Library of Congress Cataloging-in-Publication Data; CONTENTS; PREFACE; MEASURE AND INTEGRATION; Chapter 1:OPERATIONS WITH EXTRAFUNCTIONSAND INTEGRATION IN BUNDLESWITH A HYPERSPACE BASE; Abstract; 1. Introduction; 2. Seminormed Vector Spaces and Locally Convex Spaces; 3. Norm-based Sequential Hyperspaces; 4. Bundles with a Hyperspace Base; 5. Multiplication of Hypernumbers and Extrafunctions; 6. Hyperspace Extensions of Functionals and Operators; 7. Definite Integration in Hyperspaces; Conclusion; References

Chapter 2:ORTHOGONALLY SCATTERED MEASURESAND WEAK RADON-NIKODÝM DERIVATIVES1. Introduction; 2. Weak Radon-Nikodým Derivatives; 3. Orthogonally Scattered Measures and Dilation; 4. Hilbert-Schmidt Class Operator Valued Measures; References; Chapter 3:HYPERINTEGRATION IN FUNCTION SPACES; Abstract; 1. Introduction; 2. Approximations, Partitions and Covers of Topological VectorSpaces; 3. Induced Functional Integrals and Hyperintegrals in Vector; 4. Properties of Induced Hyperintegrals; Conclusion; References; Chapter 4:DIRECTIONS AND METHODS IN INTEGRATION; Abstract; 1. Introduction

2. General Classifications3. Examples; 4. Conclusion; References; EQUATIONS AND INEQUALITIES; Chapter 5:SOLITON SOLUTIONS FOR NONLINEAREVOLUTION EQUATIONS BY USINGINVERSE SCATTERING METHOD; Abstract; 1. Introduction; 2. The Solution of Gelfand-Levitan-Marchenko Equation; 3. Conclusion; References; Chapter 6:PROPERTIES OF q-INTEGRAL INEQUALITIES; Abstract; 1. Introduction; 2. Related Research; 3. Properties of q-integrals; References; Chapter 7:HYPERINTEGRAL INEQUALITIES; Abstract; 1. Introduction; 2. Integrals and Hyperintegrals in Infinite Dimensional VectorSpaces

3. Inequalities in Spaces of Hyperintegrals4. Conclusion; References; Chapter 8:GENERALIZED EQUATIONS FOR NUMERICALINTEGRATION OVER TWO DIMENSIONALDOMAINS USING QUADRATURE RULES; Abstract; 1. Introduction; 2. Numerical Integration in Two Dimensions; 3. Development of theGeneralized Equations; 4. Numerical Examples; Conclusion; Appendix A; References; OPERATORS; Chapter 9:WATSON TRANSFORM FOR BOEHMIANS; Abstract; 1. Introduction; 2. Boehmian Spaces; 3. Auxiliary Results; 4. Extended Watson Transform; References; Chapter 10:DOUBLE COMMUTANTSOF MULTIPLICATION OPERATORS ON C(K); Abstract

1. Introduction2. Continuums with DCP Property; References; Chapter 11:CURVELET TRANSFORM ON TEMPEREDBOEHMIANS; Abstract; 1. Introduction; 2. Construction of Boehmian Spaces; 3. Generalized Curvelet Transform; References; PROBABILITY; Chapter 12:HYPEREXPECTATION IN AXIOMATICAND CONSTRUCTIVE SETTINGS; Abstract; 1. Introduction; 2. Elements of the Theory of Hypernumbers; 3. Hyperexpectation; 4. Axioms for Hyperexpectation and Hyperprobabilities; Conclusion; References; Chapter 13:ON THE EFFECTIVENESS OF MIXED MODELBASED LOGISTIC REGRESSION CLASSIFIERSFOR LONGITUDINAL DATA; Abstract

1. Introduction

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

1-63482-620-5