Classic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics include Lebesque and Stieltjes integrals, Hilbert and Banach spaces, self-adjunct transformations, spectral theories for linear transformations of general type, more. Translated from 2nd French edition by Leo F. Boron. 1955 edition. Bibliography.
Here's a sample of other books in this Dover category
Theory of Hp Spaces by Peter L. Duren A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, Taylor coefficients, interpolation theory, more. 1970 edition.
General Theory of Functions and Integration by Angus E. Taylor Lucid introduction to abstract theories in analysis. Classical theory of points in Euclidean space, continuous functions, ideas of topology, more. For graduate students. 38 diagrams. Introduction. List of Special Symbols. Index.
Theory of Linear Operators in Hilbert Space by N. I. Akhiezer, I. M. Glazman This classic textbook introduces linear operators in Hilbert Space, and presents the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. Invaluable for every mathematician and physicist. 1961, 1963 edition.
Elementary Functional Analysis by Georgi E. Shilov Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.
Hardy Classes by Marvin Rosenblum, James Rovnyak Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Includes general theory of shift operators on a Hilbert space, more. Appendix. Bibliography. 1985 edition.
Banach Spaces of Analytic Functions by Kenneth Hoffman This rigorous investigation of Hardy spaces and the invariant subspace problem is suitable for advanced undergraduates and graduates, covering complex functions, harmonic analysis, and functional analysis. 1962 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.
