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

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

£75.95
Hardback Published: 30/10/1999
  • We can order this

Usually dispatched within 2 weeks

  • This item has been added to your basket
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 $T$.

Publisher: American Mathematical Society
ISBN: 9780821820490
Weight: 664 g

You may also be interested in...

Reviews

Please sign in to write a review

Your review has been submitted successfully.