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Inverse Problems for Canonical Differential Equations with Singularities
- Publisher
- Springer Basel
- Copyright
- © Springer Basel AG 2012
- ISBN
- 978-3-0348-0220-8
- Pages
- 583 –612
- DOI
- 10.1007/978-3-0348-0221-5_26
- Publisher site
- See Chapter on Publisher Site
Abstract
[A spectral theory is constructed for canonical differential systems whose Hamiltonians have selfadjoint matrix values. In contrast with the case of nonnegative Hamiltonians, eigenvalues in general can be complex, and root functions as well as eigenfunctions come into play. Eigentransforms are defined and turn out to be isometric on the span of root functions with respect to a suitably defined indefinite inner product on entire functions.]
Published: Jan 3, 2012
Keywords: Canonical differential equation; root function; pseudospectral function; spectral function; indefinite inner product; eigentransform.