Staff Members - Benha University
On the product of singular differential operators with their essential spectra in direct sum space
Journal| MESA • 2015
Publication Information
Authors
Sobhy El-sayed Ibrahim
Keywords
Productofdifferentialexpressions,regularlysolvableandwell-poseddifferentialoperators,essentialspectra, Hilbert-Schmidt integral operators.
Journal
Journal| MESA
Publisher
Not Available
Volume
6
Issue
1
Pages
101-118
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
We consider the product of general quasi-differential expressions τ1, τ2,..., τn each
of order n with complex coefficients and their formal adjoints on the interval (a, b). It is shown
in direct sum spaces L2 w (Ip), p= 1,..., N of functions defined on each of the separate
intervals with the case of one singular end-points and when all solutions of the equation [Πn
j= 1τj− λw] u= 0 and its adjoint [Πn j= 1τ+ j− λ w] v= 0 are in L2 w (a, b)(the limit circle case)
that all well-posed extensions of the minimal operator T0 (τ1, τ2,..., τn) have resolvents ...
of order n with complex coefficients and their formal adjoints on the interval (a, b). It is shown
in direct sum spaces L2 w (Ip), p= 1,..., N of functions defined on each of the separate
intervals with the case of one singular end-points and when all solutions of the equation [Πn
j= 1τj− λw] u= 0 and its adjoint [Πn j= 1τ+ j− λ w] v= 0 are in L2 w (a, b)(the limit circle case)
that all well-posed extensions of the minimal operator T0 (τ1, τ2,..., τn) have resolvents ...