The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences {cn} and {dn} of positive real numbers. By specializing {cn} and {dn}, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined. The theorems presented, in many cases, confirm or ge...

Abstract. We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ–M∗–convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ–M∗–convolution body of the n–dimensional cube is homothetic to the unit ball of ln 1 .

We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ-M∗-convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ-M∗-convolution body of the n-dimensional cube is homothetic to the unit ball of `1 .

Convolution is one of the most widely used digital signal processing operations. It can be implemented using the fast Fourier transform (FFT), with a computational complexity ofO(N logN). The undecimated discrete wavelet transform (UDWT) is linear and shift invariant, so it can also be used to implement convolution. In this paper, we propose a scheme to implement the convolution using the UDWT,...

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

1. Introduction 2. Order and type in classical complex analysis 3. Relative order and type of convex functions 4. Order and type in duality 5. The infimal convolution 6. The order of an entire function 7. A geometric characterisation of the relative order 8. An extension problem for holomorphic functions 9. Whittaker's decomposition theorem 10. Inequalities for the infimal convolution 11. Inequ...

The infimal convolution of M-convex functions is M-convex. This is a fundamental fact in discrete convex analysis that is often useful in its application to mathematical economics and game theory. M-convexity and its variant called M-convexity are closely related to gross substitutability, and the infimal convolution operation corresponds to an aggregation. This note provides a succinct descrip...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

In this paper, we present an implementation of a real-time convolver, based on Field Programmable Gate Arrays (FPGA’s) to perform the convolution operations. Main characteristics of the proposed approach are the usage of external memory to implement a FIFO buffer where incoming pixels are stored and the partitioning of the convolution matrix among several FPGA’s, in order to allow data-parallel...