Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces
Roman Lavicka
TL;DR
This paper introduces a new construction of orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces, demonstrating their completeness and orthogonality, and explores their Taylor series expansions and applications to generalized Moisil-Theodoresco systems.
Contribution
It provides an alternative construction of orthogonal bases that form complete Appell systems for Hodge-de Rham solutions, extending previous Gelfand-Tsetlin methods.
Findings
Bases form complete orthogonal Appell systems
Explicit construction of bases for generalized Moisil-Theodoresco systems
Analysis of Taylor series expansions of these bases
Abstract
Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this paper, we give another construction of these bases and, mainly, we show that the bases even form complete orthogonal Appell systems. Moreover, we study the corresponding Taylor series expansions. As an application, we construct quite explicitly orthogonal bases for homogeneous solutions of an arbitrary generalized Moisil-Theodoresco system.
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
TopicsMathematical Analysis and Transform Methods · Algebraic and Geometric Analysis · Advanced Numerical Analysis Techniques