On a solution of the Cauchy problem in the weighted spaces of Beurling ultradistributions

Abstract

© Copyright 2015 Rocky Mountain Mathematics Consortium. Results of Da Prato and Sinestrari [6] on differential operators with non-dense domain but satisfying the Hille-Yosida condition, are applied in the setting of Beurling weighted spaces of ultradistributions DLp'(s) ((0,T) × U), where U is open and bounded set in ℝd. For this purpose, the new structural theorems were given for DLp'(s) ((0,T) × U). Then a class of the Cauchy problems in the general setting of such spaces of ultradistributions is analyzed.