Christoffel-Darboux kernels in several real variables. (English) Zbl 1521.42022
Summary: The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three-term relation reformulated for this purpose. As suggestive examples of orthogonality, we propose to discuss the two simple algebraic cases: the unit circle and the Bernoulli lemniscate.
MSC:
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
polynomials in several variables; orthogonal polynomials; three-term relation; Favard’s theorem; ideal of polynomials; Christoffel-Darboux formulaReferences:
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