The Support Theorem For Ultradistributions Of Beurling Type

The theories of partial differential equation have got remarkable development because of the appearance of distribution theory. Since the eighties of nineteen century, Some schol-ars introduced the concepts of w-ultradifferentiable function and w-ultradistributions in order to solve the various problems that appeared in the theory of differential equations. These have extended the theories of distributions.The supporting theory for ultradistributions is a problem that relates to the struc-ture and characteristics of ultradistributions. Because of the complexity of the space of w-ultradistributions, the study of supporting set for corresponding function is very difficult.In this paper, we give one result about realanalytic support set supp A’(u) for w-ultradistributions u of Beurling type, using the concept of*-support introduced in T.Heinrich and R.Meise[18] and reference to the methods and technique used in the study of ultradistributions in the existing references.Theorem Let ω be a weight function which satisfies ω(t)=o(t) as t tends to infinity. Then for each u∈ε’(ω)(RN) the set supp A’(u) is (ωj)-upporting for u.In the proof of theorem we obtain a decomposition method of w-ultradistributions, using this method we can discuss the problem of decomposition of ω-ultradistributions of Roumieu type and support problem.This thesis is divided into three chapters, the main contents are as follows:In Chapter1, we introduces the research background and current situation of ultra-distributions, and the contents and methods are used in the paper.In chapter2, we give concepts, notations, and the related preparatory lemmas and its results are used in the paper.In Chapter3, we give the result of the support theorem for ultradistributions of Beurling type, useing the decomposition of ultradistributions.