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The Gelfand–Tsetlin bases for Hodge–de Rham systems in Euclidean spaces
Author(s) -
Delanghe Richard,
Lávička Roman,
Souček Vladimír
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1563
Subject(s) - mathematics , homogeneous , euclidean geometry , pure mathematics , euclidean space , space (punctuation) , homogeneous polynomial , polynomial , basis (linear algebra) , algebra over a field , orthogonal polynomials , construct (python library) , mathematical analysis , combinatorics , matrix polynomial , geometry , linguistics , philosophy , computer science , programming language
The main aim of this paper is to construct explicitly orthogonal bases for the spaces H k s ( R m ) 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. Actually, we describe even the so‐called Gelfand–Tsetlin bases for such spaces in terms of Gegenbauer polynomials. As an application, we obtain an algorithm on how to compute an orthogonal basis of the space of homogeneous solutions for an arbitrary generalized Moisil–Théodoresco system in R m . Copyright © 2012 John Wiley & Sons, Ltd.