Complete orthogonal Appell systems for spherical monogenics
R. Lavicka
TL;DR
This paper demonstrates that Gelfand-Tsetlin bases form complete orthogonal Appell systems for spherical monogenics in any dimension and explores their Taylor series expansions, extending known results from dimension 3.
Contribution
It establishes the generalization of Appell systems for spherical monogenics across all dimensions and analyzes their Taylor series expansions.
Findings
Gelfand-Tsetlin bases form complete orthogonal Appell systems in any dimension.
Results extend known 3D properties to higher dimensions.
Provides Taylor series expansions for monogenic functions.
Abstract
In this paper, we investigate properties of Gelfand-Tsetlin bases mainly for spherical monogenics, that is, for spinor valued or Clifford algebra valued homogeneous solutions of the Dirac equation in the Euclidean space. Recently it has been observed that in dimension 3 these bases form an Appell system. We show that Gelfand-Tsetlin bases of spherical monogenics form complete orthogonal Appell systems in any dimension. Moreover, we study the corresponding Taylor series expansions for monogenic functions. We obtain analogous results for spherical harmonics as well.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic and Geometric Analysis · Advanced Topics in Algebra · Nonlinear Waves and Solitons