Functional Analysis and Applications 1e

Hemant Kumar Pathak

ISBN 10: 8195637906 / ISBN 13: 9788195637904

Editore: Scienger Draft, 2022

Riguardo questo articolo

PRINT ON DEMAND.

Codice articolo 18404336027

Dati bibliografici

• Titolo: Functional Analysis and Applications 1e
• Editore: Scienger Draft
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 8195637906
• ISBN 13: 9788195637904
• Rilegatura: Rilegato
• Condizione: New

Descrizione articolo

Riassunto

Graduate Texts in Mathematics 1

Hemant Kumar Pathak

Functional Analysis and Applications

 

This textbook discusses all useful topics in functional analysis and applications. It contains complete definitions of topics well-explained by suitable examples, explanations, and proofs throughout the book. The book studies major topics on normed linear spaces, bounded linear functionals, Banach spaces, Hahn-Banach theorem, reflexive spaces, open mapping theorem, closed graph theorem, Banach Steinhaus theorem, spaces of  bounded linear functionals, weak and weak* topologies, Hilbert spaces, Riesz representation theorem, Lax-Milgram lemma, Banach algebra, the spectrum and the Gelfand-Mazur theorem, commutative Banach algebra, differentiation and integration In Banach spaces, variational methods and optimizations, approximation and optimization, operator theory, nonlinear operators and applications, spectral theory, Sturm-Liouville system and Fredholm alternative, fixed point theory, Banach contraction principle, Brouwer's fixed point theorem, Schauder's fixed point theorem, variational inequalities and applications, frames and bases in Hilbert spaces, frames and bases in Banach spaces.

 

This book Is designed as a textbook for a two-semester course in functional analysis, as well as for a first semester course in functional analysis at the lower undergraduate level. The book Is also accessible to junior mathematics majors who have studied advanced calculus or multivariable calculus. The essential prerequisites for reading this book are quite minimal: not much more than a stiff course in analysis, advanced calculus, and abstract algebra.