Szwarc, Ryszard Chain sequences and compact perturbations of orthogonal polynomials. (English) Zbl 0807.42018 Math. Z. 217, No. 1, 57-71 (1994). 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. Reviewer: R.Szwarc (Wrocław) Cited in 7 Documents MSC: 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 39A70 Difference operators Keywords:compact perturbations; chain sequences; quadratic transformations; growth of orthogonal polynomials PDFBibTeX XMLCite \textit{R. Szwarc}, Math. Z. 217, No. 1, 57--71 (1994; Zbl 0807.42018) 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.