Functional analysis. 6th ed. (English) Zbl 0435.46002

Yosida, Kosaku

Grundlehren der mathematischen Wissenschaften, 123. Berlin-Heidelberg-New York: Springer-Verlag. XII, 501 p. DM 69.00; $ 40.60 (1980).

MSC:

46A03	General theory of locally convex spaces
46Bxx	Normed linear spaces and Banach spaces; Banach lattices
46A30	Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46A08	Barrelled spaces, bornological spaces
46Cxx	Inner product spaces and their generalizations, Hilbert spaces
46A04	Locally convex Fréchet spaces and (DF)-spaces
46A20	Duality theory for topological vector spaces
46Fxx	Distributions, generalized functions, distribution spaces
47F05	General theory of partial differential operators
46J05	General theory of commutative topological algebras
46A55	Convex sets in topological linear spaces; Choquet theory
47D03	Groups and semigroups of linear operators
47D07	Markov semigroups and applications to diffusion processes
28D05	Measure-preserving transformations
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis

Keywords:

Mikusinski’s operational calculus; representation of vector lattices; Banach spaces; Hilbert spaces; spaces of distributions; Stone- Weierstraß theorem; Baire theorem; Frechet spaces; Baire-Hausdorff theorem; uniform-boundedness theorem; open-mapping; closed-graph theorems; Riesz’ representation theorem; Hahn-Banach theorem; duality; Bochner integral; Eberlein theorem; Fourier transforms; differential equations; Paley-Wiener theorem; hypoellipticity; resolvent; spectrum; semigroups; compact operators; Riesz theory; Dirichlet problem; normed rings and spectral representation; Tauberian theorem; extremal points; Krein-Mil’man theorem; ergodic theory; diffusion theory; equation of evolution

Citations:

Zbl 0286.46002; Zbl 0126.115