Carleman's inequality for Hilbert-Schmidt operators and its generalizations for Schatten-von Neumann operator ideals (see ) are shown to be sharp in a certain sense. Explicit classes of extremizing operators are found on which the generalized Carleman inequalities turn to asymptotic equalities. Applications are made to a priori estimation of the solutions of Fredholm and Volterra first- and second kind integral equations and to perturbation and error analysis. Some further generalizations are considered which extend the applications to singular integral equations, pseudodifferential equations and analytic functions of operator argument.
We characterize a class of hyperbolic cylinders of the de Sitter spacetime as the only complete non-compact spacelike hypersurfaces with constant lowest mean curvature and having more than one topological end.
The aim of this paper is to describe the Riemann-Roch map on affine schemes associated with Noetherian local rings. The Riemann-Roch theorem on singular affine schemes is one of the powerful tools in the commutative ring theory. Our main theorem enables us to calculate the Riemann-Roch maps under some assumption.
We completely determine a class of Bohman-Korovkin-Wulbert operators from a function space on a compact Hausdorff space into the Banach space of continuous complex-valued functions on another space with respect to the special test functions.
We construct a Hilbert space with a reproducing kernel by using a measure which is not positive. The space is unitarily isomorphic to a Hilbert space on the spherical sphere under the Fourier transformation. Then we study Poisson transform of Sobolev space on the n-dimensional unit sphere.