By Gerardo Chacón,Humberto Rafeiro,Juan Camilo Vallejo

ISBN-10: 3110441918

ISBN-13: 9783110441918

This textbook on useful research deals a quick and concise advent to the topic. The booklet is designed in any such manner as to supply a gentle transition among trouble-free and complex themes and its modular constitution enables a simple assimilation of the content material. ranging from a devoted bankruptcy at the axiom of selection, next chapters disguise Hilbert areas, linear operators, functionals and duality, Fourier sequence, Fourier rework, the fastened aspect theorem, Baire different types, the uniform bounded precept, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, vulnerable topologies and reflexivity, operators in Hilbert areas, spectral thought of operators in Hilbert areas, and compactness. each one bankruptcy ends with practicable problems.

The booklet is appropriate for graduate scholars, but in addition for complex undergraduates, in arithmetic and physics.

**Contents:**

List of Figures

Basic Notation

Choice Principles

Hilbert Spaces

Completeness, finishing touch and Dimension

Linear Operators

Functionals and twin Spaces

Fourier Series

Fourier Transform

Fixed aspect Theorem

Baire classification 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 concept of Operators on Hilbert Spaces

Compactness

Bibliography

Index