Abstract
The paper deals with the study of a matrix method of summation which is stronger than all the Cesàro summation methods and which assures the uniform summation of the Fourier-Jacobi series attached to continuous functions.
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Berens, H., Xu, Y.: On Bernstein-Durrmeyer polynomials with Jacobi weights. In: Chui, C.K. (ed.) Approximation Theory and Functional Analysis, pp. 25–46. Academic Press, Boston (1991)
Chandra, P.: Absolute Nörlund summability of Fourier-Jacobi series at frontier point. J. Indian Acad. Math. 16(2), 135–144 (1994)
Derriennic, M.M.: Sur l’approximation de fonctions intégrables sur \([0,\,1]\) par des polynômes de Bernstein modifiés. J. Approx. Theory 31(4), 325–343 (1981)
Durrmeyer, J.L.: Une formule d’inversion de la transformée de Laplace: applications à la théorie des moments. Thèse de 3ème cycle, Faculté des Sciences Univ. Paris (1967)
Gupta, D.P.: On a local property of absolute summability for expansions of Fourier-Jacobi class. J. London Math. Soc., II. Ser. 4 4(2), 337–345 (1971)
Osilenker, B.: Fourier Series in Orthogonal Polynomials. Word Scientific, Singapore, New Jersey, London, Hong Kong (1999)
Păltănea, R.: Sur un operateur polynomial défini sur lénsemble des fonctions intégrables. Prepr. Babeş Bolyai Univ., Fac. Math. Phys., Res. Semin. 2, 101–106 (1983)
Păltănea, R.: Une propriété d’extremalité des valeurs propres des opérateurs polynômiaux de Durrmeier généralisés. L’Analyse Numér. et la Th. de l’Approx. 15(1), 57–64 (1986)
Păltănea, R.: Approximation Theory Using Positive Linear Operators. Birkhaüser, Boston (2004)
Petersen, G.M.: Regular Matrix Transformations. McGraw-Hill, New York (1966)
Singh, L.B.: On absolute summability of Fourier-Jacobi series. An. Univ. Timisoara Seria St. Matematica 22(1–2), 89–99 (1984)
Szegő, G.: Orthogonal Polynomials, 4th edn. American Mathematical Society, Providence, Rhode Island (1975)
Thorpe, B.: Nörlund summability of Jacobi and Laguerre series. J. Reine Angew. Math. 276, 137–141 (1975)
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We thanks to the anonymous reviewer for the pertinent remarks which lead to a better presentation of the paper.
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Meleşteu, A.D., Păltănea, R. On a Method for Uniform Summation of the Fourier-Jacobi Series. Results Math 77, 153 (2022). https://doi.org/10.1007/s00025-022-01703-7
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DOI: https://doi.org/10.1007/s00025-022-01703-7