Spectral properties of a certain class of Carleman operators. (English) Zbl 1164.05037

Bahri, S. M.

Arch. Math., Brno 43, No. 3, 163-175 (2007).

Summary: The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space \(L^{2}( X,\mu ) \) and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of \(A\) and then using the Stieltjes inversion formula.

MSC:

05C38	Paths and cycles
15A15	Determinants, permanents, traces, other special matrix functions
05A15	Exact enumeration problems, generating functions
15A18	Eigenvalues, singular values, and eigenvectors

Keywords:

spectral theory; integral operator; defect indices