We determine the Hilbert-Kunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized Hilbert-Kunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of HilbertKunz functions of plane cubics. Combining these results with the calculation of the (generalized) Hilbert-Kunz function of Cayley’s...

This paper considers metric projections onto a closed subset S of a Hilbert space. If the set S is convex, then it is well known that the corresponding metric projections always exist, unique and directionally differentiable at boundary points of S. These properties of metric projections are considered for possibly nonconvex sets S. In particular, existence and directional differentiability of ...

It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a K-functional is needed. In the present paper, the upper bounds for the K-functional on the unit sphere are estimated with spherical harmonics approximation. The results show that convergence rate of the K-functional depends upon the smoothness of both the approximated func...

For pairs of density operators on nite dimensional Hilbert spaces we deene partial delities, prove their concavity and other properties. Partial delities characterize equivalence classes which are partially ordered in a natural way.

Some inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.

is called Fuchsian if the N ×N coefficient matrix A(λ) is a rational function of λ whose singularities are simple poles. Each Fuchsian system generates, via analytic continuation of its fundamental solution Ψ (λ) along closed curves, a representation of the fundamental group of the punctured Riemann sphere (punctured at the poles of A(λ)) in the group of N ×N invertible matrices. This represent...

In [13], Woronowicz introduced a functional calculus for normal regular operators in a Hilbert C-module. In this paper, we have translated several concepts known in Hilbert space theory to the Hilbert C-module framework. We looked for instance into the functional calculus for strictly positive elements, the Fuglede Putnam theorem in Hilbert C-modules, commuting normal regular operators, ... It ...

In this paper we present an explicit method of radial basis function approximation over Rn, using the Green's function for Laplace's equation. We prove convergence of the scheme for all functions that are continuous and of compact support. Interesting variants of formul result, in cases when lower dimensional formul are used to construct higher dimensional ones, and in cases of periodic functio...

We show that Macaulay’s Theorem, Gotzmann’s Persistence Theorem, and Green’s Theorem hold over a Veronese toric ring R. We also prove that the Hilbert scheme over R is connected; this is an analogue of Hartshorne’s theorem that the Hilbert scheme over a polynomial ring is connected. Furthermore, we prove that each lex ideal in R has the greatest Betti numbers among all graded ideals with the sa...

Abstract. In this paper we investigate some algebraic and geometric consequences which arise from an extremal bound on the Hilbert function of the general hyperplane section of a variety (Green’s Hyperplane Restriction Theorem). These geometric consequences improve some results in this direction first given by Green and extend others by Bigatti, Geramita, and Migliore. Other applications of our...