Abstract
In this paper some new results for general orthogonal polynomials on infinite intervals are presented. In particular, an answer to Problem 54 of P. Turàn [J. Approximation Theory, 29 (1980), P. 64] is given.
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References
Freud, G., “Orthogonal Polynomials,” Akadémiai Kiadó/Pergamon Press, Budapest, 1971.
Freud, G., On Hermite-Fejéer Interpolation Processes, Studia Sci. Math. Hungar. 7(1972), 307–316.
Nevai, P., “Orthogonal Polynomials,” Memoirs of the Amer. Math. Soc., 213, Amer. Math. Soc. Providence, R. I., 1979.
Nevai, P., “Géza Freud, Orthogonal Polynomials and Christoffel functions. A case study,” J. Approx. Theory 48(1986), 3–167.
Shi, Y. G., Bounds and Inequalities for General Orthogonal Polynomials on Finite Intervals, J. Approx. Theory 73(1993), 303–333.
Shi, Y. G., Bounds and Inequalities for Arbitrary Orthogonal Polynomials on Finite Intervals, J. Approx. Theory 81 (1995), 217–230.
Shi, Y. G., Mean Convergence of Hermite-Fejér Type Interpolation, Approx. Theory Appl. 9 (1993), 89–103.
Szegö, “Orthogonal Polynomials”, Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc., Providence, R. I., 1939.
Turán, P., On Some Open Problems of Approximation Theory, J. Approx. Theory 29(1980), 23–85.
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The Project Supported by National Natural Science Foundation of China.
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Yingguang, S. Orthogonal polynomials on infinite intervals and problem 54 of P. Turan. Approx. Theory & its Appl. 12, 53–61 (1996). https://doi.org/10.1007/BF02836126
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DOI: https://doi.org/10.1007/BF02836126