2. Arithmetic functions 19 2.1. Arithmetic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2. Multiplicative functions . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3. The Dirichlet convolution . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4. Examples of Dirichlet convolutions . . . . . . . . . . . . . . . . . . . 34 2.5. Möbius inversion . . . . . . . . . ....

A criterion for the solvability of systems of nonhomogeneous convolution equations in convex domains on the complex plane is obtained in terms of lower estimates for the characteristic functions of the convolution equations at their noncommon zeros. §

The symmetric-convolution multiplication (SCM) property of discrete trigonometric transforms (DTTs) based on unitary transform matrices is developed. Then as the reciprocity of this property, the novel multiplication symmetric-convolution (MSC) property of discrete trigonometric transforms, is developed.

We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

In this study we consider general linear second-order partial differential equations and we solve three fundamental equations by replacing the non-homogeneous terms with double convolution functions and data by a single convolution.

Using convolution, classes of p-valent functions with respect to symmetric conjugate points are introduced. Integral representation and closure properties under convolution of general classes with respect to (2j, k) symmetric points are investigated. AMS (MOS) Subject Classification Codes: 30C45

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite nondifferentiable points. In the previous work, this convolution method only can be ...

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

Multipath fading is a major problem of the wireless communication channel. To eliminate this fading problem and to have reliable communications in wireless channel, channel coding techniques are used. In this paper BER (bit error rate) performance is shown, by the means of Rayleigh and Rician multipath fading channels. Here the convolution encoding is used. The performance of convolution encode...

Convolution is one of the most widely used digital signal processing operations. This work aims to distribute twodimensional convolution operation across Intel’s Single-Chip Cloud Computer (SCC), an experimental processor created by Intel Labs. This platform enables experiments with varying both the data sizes and the physical parameters of the platform such as voltage, frequency, and number of...