There is a well developed theory of saturation for positive convolution operators on C*, the space of 2n-periodic and continuous functions. Up until recently, this was suitable to handle almost all the important approximation processes on C*. Now, however, some new and interesting sequences of operators have been obtained for C* by discretizing convolution operators [1], [5]. Such a discretized...

The Logarithmic Image Processing model (LIP) is a robust mathematical framework for the processing of transmitted and reflected images. It follows many visual, physical and psychophysical laws. This works presents a new formulation of a 2D–convolution of separable kernels using the LIP paradigm. A previously stated LIP–Sobel edge detector is redefined with the new proposed formulation, and the ...

The aim of this paper is to define and study a class of analytic functions related to Bazilevic type functions in the open unit disc.This class is defined by using a convolution operator and the concept of bounded radius rotation of order ρ . A necessary condition, inclusion result, arc length and some other interesting properties of this class of functions are investigated.

Rotation intertwining maps from the set of convex bodies in R into itself that are continuous linear operators with respect to Minkowski and Blaschke addition are investigated. The main focus is on Blaschke-Minkowski homomorphisms. We show that such maps are represented by a spherical convolution operator. An application of this representation is a complete classification of all even BlaschkeMi...

This report studies an abstract approach to modeling the motion of large eddies in a turbulent flow. If the Navier-Stokes equations (NSE) are averaged with a local, spatial convolution type filter, φ = gδ ∗ φ, the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which is an approximate filter inverse D(u) ...

Abstract -A complex-valued functions that are univalent and sense preserving in the unit disk U can be written in the form ( ) ( ) ( ) f z h z g z   , where U(z) and g(z) are analytic in. We will introduced the operator D which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(,, n) by generalized derivative operator of harmonic un...

The Pommiez operator (∆ f )(z) = ( f (z)− f (0))/z is considered in the space (G) of the holomorphic functions in an arbitrary finite Runge domain G. A new proof of a representation formula of Linchuk of the commutant of ∆ in (G) is given. The main result is a representation formula of the commutant of the Pommiez operator in an arbitrary invariant hyperplane of (G). It uses an explicit convolu...