Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators (Mathematical Surveys and Monographs)

Locker, John

ISBN 10: 0821820494 / ISBN 13: 9780821820490

Published by American Mathematical Society, 1999

About this Item

A monograph that develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L^2[0,1]$. It lays the mathematical foundation in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators. Series: Mathematical Surveys and Monographs. Num Pages: 252 pages, bibliography, index. BIC Classification: PBKF; PBKJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 230 x 0 x 0. Weight in Grams: 664. . 1999. Hardcover. . . . . Books ship from the US and Ireland.

Seller Inventory # V9780821820490

Bibliographic Details

• Title: Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators (Mathematical Surveys and Monographs)
• Publisher: American Mathematical Society
• Publication Date: 1999
• Language: English
• ISBN 10: 0821820494
• ISBN 13: 9780821820490
• Binding: Hardcover
• Condition: New

About this title

Synopsis

This monograph develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L^2[0,1]$. The mathematical foundation is laid in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators. An important completeness theorem is established for the Hilbert-Schmidt discrete operators. The operational calculus plays a major role in this general theory. In the second part, the spectral theory of the differential operator $L$ is developed by expressing $L$ in the form $L = T + S$, where $T$ is the principal part determined by the $n$th order derivative and $S$ is the part determined by the lower-order derivatives. The spectral theory of $T$ is developed first using operator theory, and then the spectral theory of $L$ is developed by treating $L$ as a perturbation of $T$. Regular and irregular boundary values are allowed for $T$, and regular boundary values are considered for $L$. Special features of the spectral theory for $L$ and $T$ include the following: calculation of the eigenvalues, algebraic multiplicities and ascents; calculation of the associated family of projections which project onto the generalized eigenspaces; completeness of the generalized eigenfunctions; uniform bounds on the family of all finite sums of the associated projections; and expansions of functions in series of generalized eigenfunctions of $L$ and $T$.