The Helmholtz Operator on Higher Dimensional Möbius Strips Embedded in $${\mathbb{R}^{4}}$$
Tóm tắt
In this paper we present explicit formulas for the fundamental solution to the Helmholtz operator on a higher-dimensional analogue of the Möbius strip in three real variables (embedded in
$${\mathbb{R}^{4}}$$
) with values in distinct pinor bundles. Herefore we use an approach that uses classical harmonic analysis methods combined with some Clifford analysis tools and adapt it to this special geometry. The fundamental solution is described in terms of generalizations of the Weierstrass
$${\wp}$$
-function that are adapted to the context of these geometries. As our main result we present an analytic integral representation formula to express the solutions of the inhomogeneous time-independent Klein-Gordon problem on Möbius strips.
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