On some shift invariant integral operators, univariate case

George A. Anastassiou, and Heinz H. Gonska. "On some shift invariant integral operators, univariate case." Annales Polonici Mathematici 61.3 (1995): 225-243. <http://eudml.org/doc/262320>.

@article{GeorgeA1995,
abstract = {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.},
author = {George A. Anastassiou, Heinz H. Gonska},
journal = {Annales Polonici Mathematici},
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},
language = {eng},
number = {3},
pages = {225-243},
title = {On some shift invariant integral operators, univariate case},
url = {http://eudml.org/doc/262320},
volume = {61},
year = {1995},
}

TY - JOUR
AU - George A. Anastassiou
AU - Heinz H. Gonska
TI - On some shift invariant integral operators, univariate case
JO - Annales Polonici Mathematici
PY - 1995
VL - 61
IS - 3
SP - 225
EP - 243
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/262320
ER -