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The aim of this paper is the study the Poisson integral for Hermite expansions. We present some boundary value problems related to this integral and its various modifications.
Rocznik
Tom
Strony
189--193
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Pedagogical University of Cracow, Institute of Mathematics, ul. Podchorążych 2, PL-30-084 Kraków, Poland
Bibliografia
- [1] R. A. DeVore, G. G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin 1993.
- [2] Z. Ditzian, V. Totik, Moduli of Smoothness, Springer-Verlag, New York 1987.
- [3] J. Gosselin, K. Stempak, Conjugate expansions for Hermite functions, Illinois J. Math. 38 (1994), 177-197.
- [4] G. Krech, On some approximation theorems for the Poisson integral for Hermite expansions, Anal. Math. 40 (2014), 133-145.
- [5] G. Krech, On the rate of convergence theorem for the alternate Poisson integrals for Hermite and Laguerre expansions, Ann. Acad. Paedagog. Crac. Stud. Math. 4 (2004), 103-110.
- [6] G. Krech, The Poisson integrals of functions of two variables for Hermite and Laguerre expansions, Prace Naukowe Akademii im. Jana Długosza w Częstochowie, Matematyka 16 (2011), 47-54.
- [7] G. Krech, The Voronovskaya type theorem for Poisson integrals of functions of two variables, Comment. Math. 53 (1) (2013), 23-34.
- [8] G. Krech, E. Wachnicki, Approximation by some combinations of Poisson integrals for Hermite and Laguerre expansions, Ann. Univ. Paedagog. Crac. Stud. Math. 12 (2013), 21-29.
- [9] M. A. Özarslan, O. Duman, Approximation properties of Poisson integrals for orthogonal expansions, Taiwanese J. Math. 12 (2008), 1147-1163.
- [10] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 33, Amer. Math. Soc., Providence, R.I. 1939.
- [11] G. Toczek, E. Wachnicki, On the rate of convergence and the Voronovskaya theorem for the Poisson integrals for Hermite and Laguerre expansions, J. Approx. Theory 116 (2002), 113-125.
Typ dokumentu
Bibliografia
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