Excellent treatment of subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. Includes detailed proofs of theorems, bibliography, and index of symbols. 1966 edition.
Here's a sample of other books in this Dover category
Special Functions & Their Applications by N. N. Lebedev, Richard R. Silverman Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.
Lectures on Functional Equations and Their Applications by J. Aczel Numerous detailed proofs highlight this treatment, which examines equations for functions of a single variable and those for functions of several variables. Also includes composite equations, vector and matrix equations, more. 1966 edition.
Probabilistic Metric Spaces by B. Schweizer, A. Sklar Topics include special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. 1983 edition, updated with 3 new appendixes. Includes 17 illustrations.
Orthogonal Functions by G. Sansone Covers expansion in a series of orthogonal functions and preliminary notions of Hilbert space; expansion in Fourier series and in series of Legendre polynomials and spherical harmonics; expansions in Laguerre and Hermite series.
Geometry and Convexity: A Study in Mathematical Methods by Paul J. Kelly, Max L. Weiss This text assumes no prerequisites, offering an easy-to-read treatment with simple notation and clear, complete proofs. From motivation to definition, its explanations feature concrete examples and theorems. 1979 edition.
Theory of Linear Operations by Stefan Banach, F. Jellett Written by the founder of functional analysis, this is the first text on linear operator theory. Additional topics include the calculus of variations and theory of integral equations. 1987 edition.
