Weighted function algebra on weighted flows, compactifications of weighted flows, existence and none existence

During the past decade harmonic analysis on weighted semigroups has enjoyed considerable attention, and a good deal of results have been proved in this connection. H A M Dzinotyiweyi in 1984 first introduced the concept of weighted function algebra on groups and semigroups. Let S be a locally compact Hausdorff semitopological semigroup. A mapping wS : S ? (0, ?) is called a weight function on S if wS (st) ? wS (s)wS (t). Khadem-Maboudi A A and Pourabdollah M A in 1999 study the relationship between semigroups and weighted semigroups with the introduce means, homomorphisms, and compactifications of weighted semitopological semigroups. They also show that these compactifications do not retain all the nice properties of the ordinary semigroup compactifications unless we impose some restrictions on the weight functions. In this paper, we introduce a weight function on flow (S, X, ?) as follows: Let X is a locally compact Hausdorff topological space and a mapping wX : X ? (0, ?) is called a weight function on X if wX(sx) ? wX(s)wx(x). Then transform it to weighted flow ((S, wS ), (X, wX), ?). We define them corresponding to weighted flows compactifications. We also show that these compactifications do not retain all the nice properties of the ordinary flow compactifications unless we impose some restrictions on the weight functions.