Functional Analysis

An Elementary Introduction

AvMarkus Haase

Inbunden, Engelska, 2014

Del i serien Graduate Studies in Mathematics

1 536 kr

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Beskrivning

This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts.The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.

Produktinformation

Utgivningsdatum:2014-09-30
Mått:178 x 254 x undefined mm
Vikt:844 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:372
Förlag:American Mathematical Society
ISBN:9780821891711

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Markus Haase, Delft University of Technology, The Netherlands

Recensioner i media

Markus Haase’s beautiful book lives up to its promise: it provides a well-structured and gentle introduction to the fundamental concepts of functional analysis…The presentation is clear, the applications are insightful, and the large collection of exercises allow us to deepen the study of the presented material. Graduate students, as well as interested undergraduate students can easily profit from this well-written book." - Béla Gábor Pusztai, ACTA Sci. Math

Innehållsförteckning

Inner product spaces Normed spaces Distance and approximation Continuity and compactness Banach spaces The contraction principle The Lebesgue spaces Hilbert space fundamentals Approximation theory and Fourier analysis Sobolev spaces and the Poisson problem Operator theory I Operator theory II Spectral theory of compact self-adjoint operators Applications of the spectral theorem Baire's theorem and its consequences Duality and the Hahn-Banach theorem Historical remarks Background The completion of a metric space Bernstein's proof of Weierstrass' theorem Smooth cutoff functions Some topics from Fourier analysis General orthonormal systems Bibliography Symbol index Subject index Author index