Separation of the general second order elliptic differential operator with an operator potential in the weighted Hilbert spaces

Separation for the biharmonic differential operator in the Hilbert space associated with the existence and uniqueness theorem

“…More fundamental results of separation of differential operator were obtained by Everitt and Giertz [8,9]. A number of results concerning the property referred to the separation of differential operators was discussed by Biomatov [2], Otelbaev [16], Zettle [20] and Mohamed et al [10][11][12][13][14][15]. The separation for the differential operators with the matrix potentials was first studied by Bergbaev [1].…”

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

“…More fundamental results of separation for differential operators were obtained by Everitt and Giertz [3,4]. A number of results concerning the property referred to the separation of differential operators was discussed by Biomatov [5], Otelbaev [6], Zettle [7] and Mohamed et al [8][9][10][11][12][13]. The separation for the differential operators with the matrix potential was first studied by Bergbaev [14].…”

“…Mohamed et al [13] have studied the separation for the general second order differential operator 5) in the weighted Hilbert space L 2,k (R n , H 1 ) with a positive weight function k(x) and the operator potential [18] have obtained recent results on the separation of linear and nonlinear Schrodinger-type operators with the operator potentials in Banach spaces. Furthermore,…”

Inequalities and separation for the Laplace–Beltrami differential operator in Hilbert spaces

“…A number of results concerning the property referred to the separation of differential operators was discussed by Biomatov [2], Otelbaev [14], Zettle [17] and Mohamed et al [8][9][10][11][12][13].…”

“…In [13] Mohamed and Atia have studied the separation for the general second-order elliptic differential operator…”