Spectrum and resolvent of a partial integral operator

Abstract

We consider the partial integral operator

where w(.,. ), K(.,. ,. ), φ are given functions. Norm estimates for the resolvent and bounds for the spectrum are established. Our main tool is the direct integral of Hilbert spaces and recent estimates for norms of the resolvents of compact operators and operators with the compact Hermitian components.

Keywords:

• partial integral operators
• resolvent
• spectrum
• perturbations
• direct integral of Hilbert spaces

AMS Subject Classifications:

• 47G10
• 47B10
• 45P05

Acknowledgement

This research was supported by the Kamea fund of the Israel.