Space-varying convolution often arises in the modeling or restoration of images captured by optical imaging systems. For example, in applications such as microscopy or photography the distortions introduced by lenses typically vary across the field of view, so accurate restoration also requires the use of space-varying convolution. While space-invariant convolution can be efficiently implemente...

We produce, on general homogeneous groups, an analogue of the usual Hörmander pseudodifferential calculus on Euclidean space, at least as far as products and adjoints are concerned. In contrast to earlier works, we do not limit ourselves to analogues of classical symbols, nor to the Heisenberg group. The key technique is to understand “multipliers” of any given order j, and the operators of con...

Making use of a linear operator , which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.

We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional. Mathematics Subject Classification: 45A05, 47G10, 47B34.

By making use of subordination between analytic functions and the Dziok-Srivastava operator, we introduce a new subclass of multivalent analytic functions. Such results as inclusion relationship, integral presentations and convolution properties for this function class are proved.

The purpose of the present paper is to investigate some sufficient conditions for the convolution operator I(m)f(z) belonging to the classes k−UCV (α), k−Sp(α), S∗ (λ) and C(λ).

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

Convolution is a fundamental operation in many signal and image processing applications. Since the computation and communication pattern in a conuolutzon operation is regular, a number of specaal archttectures have been designed and implemented for this operator. The Von Neumann architectures cannot meet the real-time requirements of applications that use convolution as an intermediate step. We...

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution open unit disk U. Using Hadamard product or convolution, function fs(z) is defined as involving an and expressed terms of functions. Neighborhood properties for are established. Further, by applying a previously introduced linear transformation using extended Libera in...