Geodesic
On some shift invariant integral operators, univariate case
Annales Polonici Mathematici, Tome 61 (1995) no. 3, pp. 225-243

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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.
DOI : 10.4064/ap-61-3-225-243
Keywords: global smoothness preservation, convergence to the unit with rates, Jackson type inequalities, sharp inequalities, modulus of continuity, integral operators, shift invariant operators, convolution type operators, shape preserving operators, probabilistic distribution function

George Anastassiou 1 ; Heinz Gonska 1

1 
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George Anastassiou; Heinz Gonska. On some shift invariant integral operators, univariate case. Annales Polonici Mathematici, Tome 61 (1995) no. 3, pp. 225-243. doi: 10.4064/ap-61-3-225-243

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