Functional Analysis: An Elementary Introduction (Graduate Studies in Mathematics)

Markus Haase

ISBN 10: 0821891715 / ISBN 13: 9780821891711

Editore: American Mathematical Society, Providence, 2014

Riguardo questo articolo

No Markings. Codice articolo 044891

Dati bibliografici

Titolo: Functional Analysis: An Elementary ...

Casa editrice: American Mathematical Society, Providence

Data di pubblicazione: 2014

Legatura: Hardcover

Condizione: Very Fine

Edizione: 1st Edition

Descrizione articolo

Riassunto:

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.