Lectures on functional analysis and applications
by Pugachev, V. S., (Vladimir Semenovich)
Title Statements
- Full title :Lectures on functional analysis and applications / V.S. Pugachev & I.N. Sinitsyn ; translated by I.V. Sinitsyna.
Edition Statements
- Publication Date:©1999.
Publication Statements
- Publisher(s):World Scientific
- Place of Publication:Singapore
- Language:eng
- Publication Date:©1999.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9789812815750, 9812815759
- oclc:on1020614830
- LC Classification:QA320.P844 1999
- Dewey Decimal:515.7
Table of Contents
Intro; CONTENTS; PREFACE; CHAPTER 1 SETS. SPACES. FUNCTIONS; 1.1. Functions and Mappings; 1.1.1. What is Functional Analysis; 1.1.2. Sets; 1.1.3. Spaces; 1.1.4- Sets Operations; 1.1.5. General Definition of a Function; 1.1.6. Images and Inverse Images of Sets. Inverse Mappings; 1.1.7. Properties of Inverse Mappings; 1.1.8. Relation of Order; 1.1.9. Choice Axiom; Problems; 1.2. Metric Spaces; 1.2.1. Main Properties of Spaces; 1.2.2. Definition of a Metric Space; 1.2.3. Open and Closed Sets. Vicinities of Points; 1.2.4. Convergence in a Metric Space; 1.2.5. Complete Metric Spaces.
1.2.6. Separable Metric Spaces1.2.7. Completion of a Metric Space; 1.2.8. Continuous Functions in Metric Spaces; Problems; 1.3. Linear Spaces; 1.3.1. Definition of a Linear Space; 1.3.2. Linear Dependence and Independence of Vector; 1.3.3. Subspaces. Linear Spans; 1.3-4. Quotient Spaces; 1.3.5. Norm of a Vector; 1.3.6. Normed Linear Spaces; 1.3.7. Banach Spaces; 1.3.8. Scalar Product; 1.3.9. Hilbert Spaces; 1.3.10. Algebras; 1.3.11. Spaces of Continuous Functions and Spaces of Bounded Functions; 1.3.12. Spaces of Differentiable Functions; Problems; 1.4. Linear Functions and Functionals.
1.4.1. Sets Opera…
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