arXiv subjects

Carmen J. Vanegas

Publications and source records attributed to Carmen J. Vanegas.

4 recordsLinked to original sources

arXiv2012

Rarita-Schwinger Type Operators on Spheres and Real Projective Space

In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.

math.CV↗

arXiv2011

Rarita-Schwinger Type operators on Cylinders

Here we define Rarita-Schwinger operators on cylinders and construct their fundamental solutions. Further the fundamental solutions to the cylindrical Rarita-Schwinger type operators are achieved by applying translation groups. In turn, a Borel-Pompeiu Formula, Cauchy Integral Formula and a Cauchy Transform are presented for the cylinders. Moreover we show a construction of a number of conformally inequivalent spinor bundles on these cylinders. Again we construct Rarita-Schwinger operators and their fundamental solutions in this setting. Finally we study the remaining Rarita-Schwinger type operators on cylinders.

math.AP↗

arXiv2011

Initial value problems in Clifford-type analysis

We consider an initial value problem of type $$ \frac{\partial u}{\partial t}={\cal F}(t,x,u,\partial_j u), \quad u(0,x)=ϕ(x), $$ where $t$ is the time, $x \in \mathbb{R}^n $ and $u_0$ is a Clifford type algebra-valued function satisfying ${\bf D}u=\displaystyle\sum_{j=0}^{n}λ_j(x)e_j\partial_ju = 0$, $λ_j(x)\in \mathbb{R} $ for all $j$. We will solve this problem using the technique of associated spaces. In order to do that, we give sufficient conditions on the coefficients of the operators ${\cal F}$ and ${\bf D}$, where ${\cal F}(u)= \displaystyle\sum_{i=0}^{n}A^{(i)}(x)\displaystyle\partial_iu$ for $A^{(i)}(x) \in \mathbb{R}$ or $A^{(i)}(x)$ belonging to a Clifford-type algebra, such that these operators are an associated pair.

math.CV↗

arXiv2011

Combined boundary value problems for the nonhomogeneous tri-analytic equation

In the present article we present a particular combination of boundary problems for the inhomogeneous tri-analytic equation: the Neumann-(Dirichlet-Neuman) problem and the (Dirichlet-Neumann)-Dirichlet problem. In order to obtain the solution and solvability conditions we use an iteration's process involving those corresponding to equations of lower order.

math.CV↗