×

Chain sequences and compact perturbations of orthogonal polynomials. (English) Zbl 0807.42018

For two measures which differ by a point mass relation between the corresponding difference operators are studied. Conditions are given which ensure these operators are compact perturbations of each other. An example showing that this is not true in general is provided also. The method makes use of chain sequences and quadratic transformations. Applications to growth of orthogonal polynomials are given.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
39A70 Difference operators
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Chihara, T.: Chain sequences and orthogonal polynomials. Trans. Amer. Math. Soc.104, 1–16 (1962) · Zbl 0171.32804 · doi:10.1090/S0002-9947-1962-0138933-7
[2] Chihara, T.: ”An introduction to orthogonal polynomials”, Vol. 13, Mathematics and Its Applications. Gordon and Breach, New York, London, Paris, 1978 · Zbl 0389.33008
[3] Nevai, P.: Orthogonal polynomials, Mem. Amer. Math. Soc.213 (1979)
[4] Nevai, P., Totik, V., Zhang, J.: Orthogonal polynomials: their growth relative to their sums. J. Approx. Theory67, 215–234 (1991) · Zbl 0754.42013 · doi:10.1016/0021-9045(91)90019-7
[5] Wall, H.S.: ”Analytic theory of continued fractions.” D. van Nostrand Co., New York, 1948 · Zbl 0035.03601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.