We consider parabolic SPDEs driven by purely spatial noise, and show the existence of solutions with random initial data and forcing terms. We perform error analysis for the semi-discrete stochastic finite element method applied to a class of equations with self-adjoint differential operators that are independent of time. The analysis employs the formal stochastic adjoint problem and the corres...

We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We have shown that for l̃ = 0, the system admits an 1-parameter family of self-adjoint extension and for l̃ 6= 0 but l̃ < 1 2 , it has also an 1parameter family of self-adjoint extension.

In simple electrical flow problems the Dirichlet integral of the potential function gives the electrical conductance. Moreover the Dirichlet integral of an arbitrary function satisfying the boundary condition gives an upper bound for the conductance. This last property (Dirichlet's principle) does not hold if the boundary value problem is not self-adjoint. This paper develops new algorithms for...

Let H be a symmetric operator in a separable Hilbert space H. Suppose that H has some gap J . We shall investigate the question about what spectral properties the self{adjoint extensions of H can have inside the gap J and provide methods how to construct self{adjoint extensions of H with prescribed spectral properties inside J . Under some weak assumptions about the operator H which are satised...

We study spectral properties of a nonself-adjoint problem for (2n) th order operator differentiation with nonlocal conditions representing multipoint perturbations the Birkhoff strongly regular self-adjoint conditions. establish sufficient under which system eigenfunctions is complete and, certain additional assumptions, forms Riesz basis. construct set transformation operators, each element ma...