The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L ...

Usually, the fast evaluation of a convolution integral R R f(y)g(x−y)dy requires that the functions f, g have a simple structure based on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the convolution of hp-functions in certain locally refined grids. More precisely, the convolution result is projected into some given hp-space (Gale...

Abstract We deal with complex spatial diffusion equations time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to heat-type equation where time is replaced convolution-type generalization of regularized Caputo derivative. prove that this a heat variable. This approach leads wrapped Brownian motion on circle time-changed by ...

is finite. The purpose of this paper is to provide a framework for proving inequalities of the form (1). The idea is to exploit the close relationship of the Fourier transform to the operation of convolution and then to apply techniques from the theory of positive integral operators. Although the convolution operators that arise are not necessarily positive, they are trivially majorized by posi...

A major problem of the existing curvilinear grid Line Integral Convolution (LIC) algorithm is that the resulting LIC textures may be distorted after being mapped onto the parametric surfaces, since a curvilinear grid usually consists of cells of di erent sizes. This paper proposes a way for solving the problem through using multi-granularity noise as the input image for LIC. A stochastic sampli...

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

Under special conditions an approximate wave front solution to a system of nonlinear reaction-diffusion type equations is obtained. An assumption of fast kinetics permits the system to be reformulated as a single nonlinear differential-integral equation of convolution type. If the convolution kernel has the form of a mollifier then the convolution is localized to obtain an infinite system of di...