The necessary and sufficient conditions for compactness of a matrix operator between Banach spaces is obtained by utilizing the concept of the Hausdorff measure of noncompactness. This is one of the most interesting application in the theory of sequence spaces. In this paper, the compact operators are characterized on Jordan totient sequence spaces by using the concept of the Hausdorff measure of noncompactness. [ABSTRACT FROM AUTHOR]
In this paper, we first define a new regular matrix by using the arithmetic function called Jordan totient function and study the matrix domain of this newly introduced matrix in the Banach space ℓp. After computing the dual spaces of this new space, we characterize certain matrix mappings related to this space. [ABSTRACT FROM AUTHOR]
In this paper, we consider one‐dimensional Schrödinger operators Sq on R with a bounded potential q supported on the segment h0,h1 and a singular potential supported at the ends h0, h1. We consider an extension of the operator Sq in L2R defined by the Schrödinger operator Hq=−d2dx2+q and matrix point conditions at the ends h0, h1. By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator Hq. Moreover, we provide closed‐form expressions for the eigenfunctions and associate functions in the Jordan chain given in the form of power series of the spectral parameter. The validity of our approach is proven in several numerical examples including self‐adjoint and nonself‐adjoint problems involving general point interactions described in terms of δ‐ and δ′‐distributions. [ABSTRACT FROM AUTHOR]