This paper reviews the theoretical approaches and existing models of the solar wind interaction with the Local Interstellar Cloud (LIC). Models discussed take into account the multi-component nature of the solar wind and local interstellar medium. Basic results of the modeling and their possible applications to interpretation of space experiments are summarized. Open questions of global modelin...

In the present paper we give a fractional generalization of the Lauwerier formulation of the boundary value problem of the temperature field in oil strata. The Caputo fractional derivative operator and the Laplace transform are the important tools for solving the proposed problem. By using Efros’ theorem which is a modified form of convolution theorem for Laplace transform, the solution is obta...

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on Lp(H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α1I+Sf , where Sf is the operator given by convolution with f , f ∈ Lv(H), is invertible in B(Lp(H)), then (α1I + Sf )−1 = α2I + Sg, and g ∈ Lv(H). We p...

For certain meromorphic function g and h, we study a class of functions f(z) = z−1 + ∑∞ n=1 fnz , (fn ≥ 0), defined in the punctured unit disk ∆∗, satisfying < ( (f ∗ g)(z) (f ∗ h)(z) ) > α (z ∈ ∆; 0 ≤ α < 1) . Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. Properties of an integral operator and its inverse defined on the new class is also...

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution in-tegrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this descript...

The Meda inequality for rearrangements of the convolution operator on the Heisenberg group Hn is proved. By using the Meda inequality, an O’Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator MΩ,α and fractional integral operator IΩ,α with rough kernels in the spac...

The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly ...

In this article we consider the Levy processes and the corresponding semi-group. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the properties of a wide class of Levy processes (potential, quasi-potential, the probability of the Levy process remaining within the given domain, long time b...

In this work, methods for the solution of Fredholm equations of the first kind with convolution kernel are presented, where all the functions in the integral equation are functions on the Euclidean motion group, and the convolution product is defined relative to the group operation. An application in which such equations arise is examined in detail. The properties of the Fourier transform of sc...