Cyclic Functions in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>(<Emphasis Type="Bold">R</Emphasis>),1 le <Emphasis Type="Italic">p</Emphasis> < infty期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Cyclic Functions in Lp(R),1 le p < infty

Authors:	Joseph M.?Rosenblatt mailto:jrsnbltt@math.uiuc.edu" title=" jrsnbltt@math.uiuc.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Karen L.?Shuman mailto:kshuman@math.uiuc.edu" title=" kshuman@math.uiuc.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics, University of Illinois at Urbana, Urbana, IL 61801, USA

Abstract:	Functions whose translates span L ^p(R) are called L ^p-cyclic functions. For a fixedp memb [1, infty], we construct Schwartz-class functions which are L ^r -cyclic for r > p and not L ^r-cyclic for r le p. We then construct Schwartz-class functions which are L ^r -cyclic for r ge p andnot L ^r -cyclic for r < p. The constructions differ for p memb (1, 2) and p > 2.

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