We consider the partial integral operator (Formula presented.) 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.
- Direct integral of Hilbert spaces
- Partial integral operators
ASJC Scopus subject areas
- Environmental Chemistry
- Plant Science