In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
A general scheme based on a commutation relation is proposed to give rise to a definition of generalized Toeplitz operators on a Banach space. Under suitable conditions the existence of a symbol is proved and its continuation to algebras generated by generalized Toeplitz operators is constructed. A stability theorem for the point spectrum of an operator from generalized Toeplitz algebras is established; as examples one considers the standard and operator valued Toeplitz operators on weighted Hardy...
In this paper the method of spherical harmonics (MSH) is investigated, which is one of effective methods of approximative solution of the transport equation. On a unified methodical basis, boundary conditions on the outside and inner boundaries for every -approximation of MSH are formulated. These boundary conditions coincide with Vladimirov’s conditions (for ) and Rumjancev’s conditions (for every ). Symmetrization of the system of stationary equations of MSH for every -approximation with arbitrary...