Hilbert Space Operators

This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it opens with an elementary presen

Excellent undergraduate/graduate-level introduction presents full introduction to the subject and to the Fourier series as related to applied mathematics, considers principal method of solving partial

This three-part treatment begins with background material on definitions and terminology, operators in Hilbert space, and the imprivitity theorem, advancing to considerations of the algebras of operat

This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-s

This frequently cited scholarly reference presents a unified treatment of important subjects from the theory of operators and operator algebras on Hilbert spaces and integration and representation the

Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, the