PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 61 | 3 | 225-243
Tytuł artykułu

On some shift invariant integral operators, univariate case

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and preservation of continuous probabilistic functions. Finally, four examples of very general specialized operators are presented fulfilling all the above properties; in particular, the inequalities for global smoothness preservation are proven to be sharp.
Twórcy
  • Department of Mathematics, University of Duisburg, D-47048 Duisburg, Germany
  • Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152, U.S.A.
Bibliografia
  • [1] G. Anastassiou, C. Cottin and H. Gonska, Global smoothness of approximating functions, Analysis 11 (1991), 43-57.
  • [2] G. Anastassiou, C. Cottin and H. Gonska, Global smoothness preservation by multivariate approximation operators, in: Israel Mathematical Conference Proc. 4, Weizmann Science Press, 1991, 31-44.
  • [3] G. Anastassiou and X. M. Yu, Monotone and probabilistic wavelet approximation, Stochastic Anal. Appl. 10 (1992), 251-264.
  • [4] G. Anastassiou and X. M. Yu, Convex and coconvex-probabilistic wavelet approximation, Stochastic Anal. Appl., 507-521.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv61z3p225bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.