Foundations of modern analysis. Reprint of the 1970 orig. (English) Zbl 0557.46001

Friedman, Avner

New York: Dover Publications, Inc. VI, 250 p. (1982).

This is an unaltered reprinting (with minor corrections) of the 1970 original. For a review see Zbl 0198.076.

MSC:

46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
28-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
28A25	Integration with respect to measures and other set functions
46B03	Isomorphic theory (including renorming) of Banach spaces
35D10	Regularity of generalized solutions of PDE (MSC2000)
34B27	Green’s functions for ordinary differential equations
35J25	Boundary value problems for second-order elliptic equations
28A12	Contents, measures, outer measures, capacities
28A20	Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
46B10	Duality and reflexivity in normed linear and Banach spaces
47B06	Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47B15	Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A10	Spectrum, resolvent
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
54E35	Metric spaces, metrizability

Keywords:

measure and integration; metric space; Banach space; duality; compact operators; spectral theory of bounded selfadjoint operators; in Hilbert space; Sobolev spaces; hypoellipticity; Hilbert Schmidt; operator; boundary value problem; Green function; Dirichlet; problem