Christoffel-Darboux kernels in several real variables
Dariusz Cicho\'n, Franciszek H. Szafraniec
TL;DR
This paper explores Christoffel-Darboux kernels for multivariable orthogonal polynomials, reformulating the three-term recurrence relation and providing examples on specific geometric domains.
Contribution
It introduces a reformulation of the three-term recurrence relation for multivariable orthogonal polynomials and discusses examples on the unit circle and Bernoulli lemniscate.
Findings
Reformulation of the three-term recurrence relation for multivariable cases
Explicit examples on the unit circle and Bernoulli lemniscate
Enhanced understanding of Christoffel-Darboux kernels in multiple variables
Abstract
The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose. Examples of orthogonal polynomials on the unit circle and on the Bernoulli lemniscate are discussed.
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Taxonomy
TopicsMathematical functions and polynomials · Matrix Theory and Algorithms · Nonlinear Waves and Solitons