This classic of mathematics offers advanced undergraduates, graduate students, and professionals a comprehensive exposition of unbounded linear operator theory. Its self-contained, systematic treatment covers both theory and applications to differential equations. Expressed in simple notation and a readable style, it includes examples and motivations for certain definitions and proofs. Reprint of the 1985 Dover edition.
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.
The Convolution Transform by Isidore Isaac Hirschman, David V. Widder The relation between differential operators and integral transforms is the theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, more.
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.
