In this paper severely ill-posed problems are studied which are represented in the form of linear operator equations with innnitely smoothing operators but with solutions having only a nite smoothness. It is well known, that the combination of Morozov's discrepancy principle and a nite dimensional version of the ordinary Tikhonov regularization is not always optimal because of its saturation pr...

A new algorithm is proposed for demodulating discrete-time AM-FM signals, which first interpolates the signals with smooth splines and then uses the continuous-time energy separation algorithm (ESA) based on the Teager-Kaiser energy operator. This spline-based ESA retains the excellent time resolution of the ESAs based on discrete energy operators but performs better in the presence of noise. F...

We investigate an initial boundary value problem for a second-order hyperbolic equation with only integral conditions. We show the existence, uniqueness, and continuous dependence of a strongly generalized solution. The proof is based on an energy inequality established in a nonclassical function space, and on the density of the range of the operator associated to the abstract formulation of th...

We establish small-time asymptotic expansions for heat kernels of hypoelliptic Hörmander operators in a neighborhood the diagonal, generalizing former results obtained particular by Métivier and Ben Arous. The coefficients our are identified terms nilpotentization underlying sub-Riemannian structure. Our approach is purely analytic relies on local global subelliptic estimates as well nature asy...

A simple linear smoothing operator of general order p is constructed for discretized functions. It is particularly suited for problems in numerical integration where it is necessary or desirable to suppress two-grid-interval waves. The operator is ideal in the sense that for the class of damping operators of order p, which remove two-gridinterval waves without changing the phase of any wave com...

Scale space approach turned out to be a powerful framework for image processing purposes. In this paper we introduce proposal of a scale space concept generalized for datasets of quaternions e.g trajectories representing motion capture data. We introduce equivalents of non-linear and anisotropic simplification operators which exhibit a completely new set of properties. Three groups of applicati...

We derive some basic properties for a class of discretely divergence{free nite elements which lead to a new proof of the smoothing property in a standard multigrid algorithm for solving the Stokes equations. Using appropriate grid transfer routines which are of second order accuracy and interpolate in a divergence{free way, the usual multigrid convergence is obtained. The implementation of thes...

We survey robust multigrid methods in the literature which have been developed in recent years for solving second order elliptic PDEs with nonsmooth coeecients. We highlight the key ideas of designing robust multigrid methods which are able to recover the usual multigrid eeciency for nonsmooth coeecient PDEs on structured or unstructured grids. In particular, we shall describe various approache...

Questions of solution of three-dimensional diffraction problems are considered. Each problem is formulated as a single weakly-singular integral equation of the 1st kind for a single unknown function. Discretization of these equations is realized by means of special smoothing method of integral operators kernels. Numerical solutions of systems of linear algebraic equations, approximating integra...

We prove essential self-adjointness for semi-bounded below magnetic Schrödinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This is an extension of the Povzner–Wienholtz theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cu...