FAQ

An investigation of the approximation of functions of two variables by the poisson integral for Hermite expansions

Data publikacji: 10.02.2015

Czasopismo Techniczne, 2014, Nauki Podstawowe Zeszyt 3 NP (17) 2014, s. 31 - 38

https://doi.org/10.4467/2353737XCT.14.310.3398

Autorzy

Grażyna Krech
Institute of Mathematics, Pedagogical University of Cracow, Kraków
Wszystkie publikacje autora →

Tytuły

An investigation of the approximation of functions of two variables by the poisson integral for Hermite expansions

Abstrakt

This paper presents a study of the approximation properties of the Poisson integral for Hermite expansions in the space Lp. The rate of convergence of functions of two variables by these integrals is established.

Bibliografia

Bergh J., Löfström J., Interpolation Spaces. An Introduction, Springer-Verlag, Berlin, Heidelberg, New York 1976.

DeVore R.A., Lorentz G.G., Constructive Approximation, Springer, Berlin 1993.

Ditzian Z., Totik V., Moduli of Smoothness, Springer, New York 1987.

Gosselin J., Stempak K., Conjugate expansions for Hermite functions, Illinois J. Math. 38 1994, 177-197.

Krech G., A note on the Poisson integral for Hermite expansions of functions of two variables, J. Appl. Anal. (submitted).

Krech G., 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.

Krech G., On some approximation theorems for the Poisson integral for Hermite expansions, Analysis Math. 40, 2014, 133-145.

Krech G., Wachnicki E., Approximation by some combinations of the Poisson integrals for Hermite and Laguerre expansions, Ann. Univ. Paedagog. Crac. Stud. Math. 12, 2013, 21-29.

Muckenhoupt B., Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139, 1969, 231-242.

Özarslan M.A., Duman O., Approximation properties of Poisson integrals for orthogonal expansions, Taiwanese J. Math. 12, 2008, 1147-1163.

Szegö G., Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 33, Amer. Math. Soc., Providence, R.I., 1939.

Toczek G., Wachnicki E., 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.

Informacje

Informacje: Czasopismo Techniczne, 2014, Nauki Podstawowe Zeszyt 3 NP (17) 2014, s. 31 - 38

Typ artykułu: Oryginalny artykuł naukowy

Tytuły:

Polski:

An investigation of the approximation of functions of two variables by the poisson integral for Hermite expansions

Angielski:

An investigation of the approximation of functions of two variables by the poisson integral for Hermite expansions

Autorzy

Institute of Mathematics, Pedagogical University of Cracow, Kraków

Publikacja: 10.02.2015

Status artykułu: Otwarte __T_UNLOCK

Licencja: Żadna

Udział procentowy autorów:

Grażyna Krech (Autor) - 100%

Korekty artykułu:

-

Języki publikacji:

Angielski