Functional analysis. Theory and applications. (Analyse fonctionnelle. Théorie et applications.) (French) Zbl 1147.46300

Brézis, Haïm

Collection Mathématiques Appliquées pour la Maîtrise. Paris: Masson. 248 p. (1994).

See the review of the 1983 edition in Zbl 0511.46001.

MSC:

46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
47-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
47F05	General theory of partial differential operators
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46B03	Isomorphic theory (including renorming) of Banach spaces
46B10	Duality and reflexivity in normed linear and Banach spaces
46C05	Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
47B06	Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47E05	General theory of ordinary differential operators
47D03	Groups and semigroups of linear operators
47A53	(Semi-) Fredholm operators; index theories
35K05	Heat equation
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J10	Schrödinger operator, Schrödinger equation

Keywords:

heat equation; Laplace and Poisson equation; Dirichlet and Neumann problems; Cauchy problem; Sobolev spaces; elliptic equations; Lax-Milgram theorem; Hille-Yosida theorem; wave equation; compact operators; Riesz-Fredholm theory; spectral decomposition; selfadjoint compact operators; \(L^p\)-spaces; compactness

Citations:

Zbl 0511.46001