Quantcast

Polynomial ultradistributions on R+d

Research paper by Oleh Lopushansky, Sergii Sharyn

Indexed on: 19 Mar '16Published on: 26 Nov '09Published in: Topology



Abstract

Let <img height="18" border="0" style="vertical-align:bottom" width="78" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si2.gif">G+′=G′(R+d) stand for Roumieu ultradistributions with supports in the positive cone <img height="18" border="0" style="vertical-align:bottom" width="20" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si3.gif">R+d. Throughout <img height="16" border="0" style="vertical-align:bottom" width="39" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si4.gif">P(G+′) denotes the algebra of continuous scalar polynomials on the space <img height="16" border="0" style="vertical-align:bottom" width="18" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si5.gif">G+′. We investigate the dual pair <img height="17" border="0" style="vertical-align:bottom" width="101" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si6.gif">〈P′(G+′)∣P(G+′)〉 generated by the algebra <img height="16" border="0" style="vertical-align:bottom" width="39" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si7.gif">P(G+′) and by its strong dual <img height="16" border="0" style="vertical-align:bottom" width="42" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si8.gif">P′(G+′). Properties of the polynomially extended operational calculus and the semigroups of shifts along the cone <img height="18" border="0" style="vertical-align:bottom" width="20" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0040938309000172-si9.gif">R+d are considered.