Multi-Interval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra

by William N. Everitt, L. Markus

A multi-interval quasi-differential system $\{I_{r}, M_{r}, w_{r}: r\in\Omega\}$ consists of a collection of real intervals, $\{I_{r}\}$, as indexed by a finite, or possibly infinite index set $\Omega$ (where $\mathrm{card} (\Omega)\geq\aleph_{0}$ is permissible), on which are assigned ordinary or quasi-differential expressions $M_{r}$ generating unbounded operators in the Hilbert function spaces $L_{r} DEGREES{2}\equiv L DEGREES{2}(I_{r};w_{r})$, where $w_{r}$ are given, non-negative weight functions. For each fixed $r\in\Omega$ assume that $M_{r}$ is Lagrange symmetric (formally self-adjoint) on $I_{r}$ and hence specifies minimal and maximal closed operators $T_{0, r}$ and $T_{1, r}$, respectively, in $L_{r} DEGREES{2}$. However the theory does not require that the corresponding deficiency indices $d_{r} DEGREES{-}$ and $d_{r} DEGREES{+}$ of $T_{0, r}$ are equal (for example the symplectic excess $Ex_{r}=d_{r} DEGREES{+}-d_{r} DEGREES{-}\neq 0$), in which case there will not exist a

64 pages, Mass Market Paperback

First published March 1, 2001

About the author

William Norrie Everitt