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An interpolation-theoretical characterization of the classical orthogonal polynomials

An interpolation-theoretical characterization of the classical orthogonal polynomials Acta Mathematica Academiae Seientiarum IIungaricae Tomus 26 (1--2), (1975), 163--169. AN INTERPOLATION-THEORETICAL CHARACTERIZATION OF THE CLASSICAL ORTHOGONAL POLYNOMIALS By I. JO0 (Budapest) 1. The Jacobi, the Laguerre and the Hermite polynomials together form the so called "classical" orthogonal polynomials (in the strict sense of'the word). They are characterized by their several particular properties (see ACZs [1], FELDMaNN [2], MIKOLAS [3], LESKY [4], HAHN [5], KRALL [6], CSASZ~R [7]). An interpolation theoretical characterization was given by EG]~RVARY and TURIN [8], [9J for the Legendre and Hermite polynomials, further for the Laguerre polynomials with the parameter 0. BALAZS [1(3] characterized the ultraspherical polynomials and Jo6 [11] characterized the Laguerre polynomials with the parameter 1 in a similar way. The method appeared first in [8] seems very useful on several parts of the approxi- mation theory (see for example FRZUD [13] Theorem (IIL1.6)). In the present paper we shall give an interpolation-theoretical characterization for all Jacobi and Laguerre polynomials. Adding these results to the results of [9], [10] we obtain a complete interpolation-theoretical chalacterization of all classical orthogonal polynomials. 2. Let (1) a< :q < x2 <... < x,,< b be n points in (a, b) and let the fundamental interpolation polynomials http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

An interpolation-theoretical characterization of the classical orthogonal polynomials

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF01895959
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Abstract

Acta Mathematica Academiae Seientiarum IIungaricae Tomus 26 (1--2), (1975), 163--169. AN INTERPOLATION-THEORETICAL CHARACTERIZATION OF THE CLASSICAL ORTHOGONAL POLYNOMIALS By I. JO0 (Budapest) 1. The Jacobi, the Laguerre and the Hermite polynomials together form the so called "classical" orthogonal polynomials (in the strict sense of'the word). They are characterized by their several particular properties (see ACZs [1], FELDMaNN [2], MIKOLAS [3], LESKY [4], HAHN [5], KRALL [6], CSASZ~R [7]). An interpolation theoretical characterization was given by EG]~RVARY and TURIN [8], [9J for the Legendre and Hermite polynomials, further for the Laguerre polynomials with the parameter 0. BALAZS [1(3] characterized the ultraspherical polynomials and Jo6 [11] characterized the Laguerre polynomials with the parameter 1 in a similar way. The method appeared first in [8] seems very useful on several parts of the approxi- mation theory (see for example FRZUD [13] Theorem (IIL1.6)). In the present paper we shall give an interpolation-theoretical characterization for all Jacobi and Laguerre polynomials. Adding these results to the results of [9], [10] we obtain a complete interpolation-theoretical chalacterization of all classical orthogonal polynomials. 2. Let (1) a< :q < x2 <... < x,,< b be n points in (a, b) and let the fundamental interpolation polynomials

Journal

Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals

Published: May 21, 2016

References

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