Some properties and applications of the Teodorescu operator associated to the Helmholtz equation

Abstract

In this paper, we first define the Teodorescu operator related to the Helmholtz equation and discuss its properties in quaternion analysis. Then we propose the Riemann boundary value problem related to the Helmholtz equation. Finally we give the integral representation of the boundary value problem by using the previously defined operator.

The Riemann boundary value problem related to the time-harmonic Maxwell equations

“…For the above purpose, we introduce the N matrix operator which establishes the relationship between the Helmholtz equation and the time-harmonic Maxwell equations. In [15], we discuss some properties of Teodorescu operator and the Riemann boundary value problem related to the Helmholtz equation. By using the N matrix operator and the conclusions in [15], we give the integral representation of the solution for the Riemann boundary value problem related to the time-harmonic Maxwell equations.…”

“…In [15], we discuss some properties of Teodorescu operator and the Riemann boundary value problem related to the Helmholtz equation. By using the N matrix operator and the conclusions in [15], we give the integral representation of the solution for the Riemann boundary value problem related to the time-harmonic Maxwell equations. The structure of this paper is as follows: In Sect.…”

“…L p (B) , p ≥ 1. In [15], we introduce the Teodorescu operator related to the Helmholtz equation as follows:…”

“…In [15], we studied the properties of the above integral operators and obtained the integral representation of the solution for the Riemann boundary value problem related to the Helmholtz equation. The specific results are as follows.…”

“…Hile GN [2] and Gilbert RP et al [3] studied some properties of the Teodorescu operator in n-dimensional Euclidean space and higher-dimensional complex spaces. Du JY, Yang PW, Qiao YY, Taira K and Wang LP et al studied some properties and boundary value problems associated with the Teodorescu operator in quaternion analysis and Clifford analysis (see [4][5][6][7][8][9][10][11][12][13][14][15][16]).…”