On a system of orthogonal polynomials with the weight \( (1-x^2-y^2)^\beta\), \( \beta>-1\), on the disk~\( x^2+y^2\leq 1\) (Q2719438)
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scientific article; zbMATH DE number 1609683
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a system of orthogonal polynomials with the weight \( (1-x^2-y^2)^\beta\), \( \beta>-1\), on the disk~\( x^2+y^2\leq 1\) |
scientific article; zbMATH DE number 1609683 |
Statements
25 June 2001
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orthogonal polynomials with weight
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On a system of orthogonal polynomials with the weight \( (1-x^2-y^2)^\beta\), \( \beta>-1\), on the disk~\( x^2+y^2\leq 1\) (English)
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In this paper a system of polynomials of group-theoretic nature is examined. Characteristics of these polynomials are treated by the methods of representation theory using representation of the group \(MU(n)\) of all motions of the \(n\)-dimensional Euclidean complex space. It is noted that various polynomial systems being orthogonal for the disk \( x^2+y^2\leq 1 \) with the weight \( (1-x^2-y^2)^\beta\), \( \beta>-1,\) are defined and studied, but in the case of two and more arguments the weight function does not determine unambiguously the orthogonal system.
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