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Pencils of differential operators containing the eigenvalue parameter in the boundary conditions
- Source :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 133:893-917
- Publication Year :
- 2003
- Publisher :
- Cambridge University Press (CUP), 2003.
-
Abstract
- The paper deals with linear pencils N − λP of ordinary differential operators on a finite interval with λ-dependent boundary conditions. Three different problems of this form arising in elasticity and hydrodynamics are considered. So-called linearization pairs (W, T) are constructed for the problems in question. More precisely, functional spaces W densely embedded in L2 and linear operators T acting in W are constructed such that the eigenvalues and the eigen- and associated functions of T coincide with those of the original problems. The spectral properties of the linearized operators T are studied. In particular, it is proved that the eigen- and associated functions of all linearizations (and hence of the corresponding original problems) form Riesz bases in the spaces W and in other spaces which are obtained by interpolation between D(T) and W.
Details
- ISSN :
- 14737124 and 03082105
- Volume :
- 133
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Accession number :
- edsair.doi...........d3d83336d9c011017b757cf8635d6a61