Boundary value problems for Poisson integrals for Hermite expansions

• Autorzy: Krech G.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

boundary value problems; Poisson integral; Hermite expansions

PL

zagadnienia brzegowe; całka Poissona; wielomiany Hermite'a

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2014
• Tom: Vol. 19
• Strony: 189--193
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Krech G.

• Pedagogical University of Cracow, Institute of Mathematics, ul. Podchorążych 2, PL-30-084 Kraków, Poland

Bibliografia

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• [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.