Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators

ISBN-13: 9780821820490 / Angielski / Twarda / 1999

John Locker

Opis

This monograph develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L 0,1]$. 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.