Elements of functional analysis : from Banach spaces to elliptic problems / José M. Mazón

Format:

Book

Author/Creator:

Mazón, José M., 1953- author.

Series:

Universitext 2191-6675

Universitext, 2191-6675

Language:

English

Subjects (All):

Functional analysis.

Physical Description:

1 online resource : illustrations.

illustration

Place of Publication:

Cham, Switzerland : Springer, [2026]

Summary:

"Functional analysis can be understood as a shift, within mathematical analysis, from the study of individual functions to the study of function spaces, their structures, and the mappings between them. Developed primarily during the 20th century, this theory continues to be essential for the study of partial differential equations. This textbook begins with the general theory: Banach spaces, Hilbert spaces, and the spectral theory of operators. It then proceeds to a thorough account of Schwartz’s Theory of Distributions and some of its applications, such as the fundamental solutions of classical operators in physics, the Malgrange–Ehrenpreis Theorem, hypoelliptic operators, and the Schrödinger equation. An extensive chapter is dedicated to the study of Sobolev spaces, including functions of bounded variation. These spaces provide the appropriate framework for the study of elliptic boundary value problems, which form the focus of the final chapter. Drawing on years of teaching experience, this textbook is ideal for introductory graduate courses, featuring historical notes and numerous exercises that reinforce learning and complement the core material"-- Springer Nature Link

Contents:

Brief historical notes

Banach spaces

Hilbert spaces

Spectral theory of operators

Theory of distributions

Sobolev spaces

Elliptic boundary value problems

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed September 2, 2026)

Other Format:

Print version: Mazón, José M., 1953- Elements of functional analysis

ISBN:

9783032292100

3032292107

OCLC:

1610818933

Access Restriction:

Restricted for use by site license