Orthogonal Systems of Eigenvectors and Associated Vectors for Symmetric Holomorphic Operator Functions
✍ Scribed by Manfred Möller
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 962 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
In Banach spaces the principal parts of the inverse of a holomorphic Fredholm valued operator function can be written as sums of tensor products of biorthogonal canoncial systems of eigenvectors and associated vectors of the operator function and its adjoint. If we impose a symmetry condition on the operator function, then for real eigenvalues the eigenvectors and associated vectors of the operator function and its adjoint coincide at this point. We shall show that we can always choose a suitable canonical system of eigenvectors and associated vectors which is orthogonal, i.e., biorthogonal to itself. An application to elliptic differential operators is given.