Descripciones mejoradas de Syndetics:

An advanced textbook for an introductory course in functional analysis. Includes revision of the work on metric and topological linear spaces and reflexivity and weak convergence. New material on the Wiener algebra of absolutely convergent Fourier series and on weak topologies has been added. A new final chapter includes elementary applications of functional analysis to differential and integral equations. Annotation copyrighted by Book News, Inc., Portland, OR

Tabla de contenidos provista por Syndetics

• Preface to the second edition
• Preface to the first edition
• Part I Basic Set Theory and Analysis
• 1 Sets and functions
• 2 Real and complex numbers
• 3 Sequences of functions, continuity, differentiability
• 4 Inequalities
• Part II Metric and Topological Spaces
• 1 Metric and semimetric spaces
• 2 Complete metric spaces
• 3 Some metric and topological concepts
• 4 Continuous functions on metric and topological spaces
• 5 Compact sets
• 6 Category and uniform boundedness
• Part III Linear and Linear Metric Spaces
• 1 Linear spaces
• 2 Subspaces, dimensionality, factorspaces, convex sets
• 3 Metric linear spaces, topological linear spaces
• 4 Basis
• Part IV Normed Linear Spaces
• 1 Convergence and completeness
• 2 Linear operators and functionals
• 3 The Banach-Steinhaus theorem
• 4 The open mapping and closed graph theorems
• 5 The Hahn-Banach extension
• 6 Weak topology and weak convergence
• Part V
• 1 Algebras and Banach algebras
• 2 Homomorphisms and isomorphisms
• 3 The spectrum and the Gelfand-Mazaur theorem
• 4 The Weiner algebra
• Part VI Hilbert Space
• 1 Inner product and Hilbert spaces
• 2 Orthonormal sets
• 3 The dual space of a Hilbert space
• 4 Symmetric and compact operators
• Part VII Applications
• 1 Differential and integral problems
• 2 The Sturm-Liouville problem
• 3 Matrix transformations in sequence spaces
• Appendix
• Bibliography
• Index