Functional Analysis: A Terse Introduction, 1st Edition eBook

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This textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems. The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents: List of Figures Basic Notation Choice Principles Hilbert Spaces Completeness, Completion and Dimension Linear Operators Functionals and Dual Spaces Fourier Series Fourier Transform Fixed Point Theorem Baire Category Theorem Uniform Boundedness Principle Open Mapping Theorem Closed Graph Theorem Hahn–Banach Theorem The Adjoint Operator Weak Topologies and Reflexivity Operators in Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces Compactness Bibliography Index

This is a digital product.

Functional Analysis: A Terse Introduction 1st Edition is written by Gerardo Chacón; Humberto Rafeiro; Juan Camilo Vallejo and published by De Gruyter. The Digital and eTextbook ISBNs for Functional Analysis are 9783110433647, 3110433648 and the print ISBNs are 9783110441918, 3110441918. Additional ISBNs for this eTextbook include 9783110441925.