Báo Cáo Báo cáo hóa học ON DIFFERENCE EQUATION WITH GENERALIZED DILATION PAVEL PLASCHINSKY

ON DIFFERENCE EQUATION WITH GENERALIZED DILATION PAVEL PLASCHINSKY Received 22 July 2004; Revised 24 January 2005; Accepted 27 January 2005 We investigate the functional equation with generalized dilation in the special weighted functional spaces. We provide some sufficient conditions for the existence of the inversion operator in the same form and consider several examples. Copyright © 2006 Pavel Plaschinsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Consider the functional equation with generalized dilation: ∞ a(n,x)nντ f nτ x = g(x), x ∈ (0; ∞), τ,ν ∈ R, (1.1) n =1 where a(n,x) is bounded almost everywhere on (0; ∞) for arbitrary natural n, and the sequence (an ) of their L∞ -norms belongs to l1 . The equations of this type are used in many areas of physics [4, 5],