Investigation of special Banach spaces of holomorphic, harmonic and real analytic functions

我想邀请Ludkovsky博士教授（莫斯科）也在帕德博恩大学做客三个月。我们想继续研究四元数上的m<s:1> ntz空间和Banach空间。特别是，我们目前起草的三篇论文将完成并提交发表。我们在这里证明了关于自反L_p范数的所有m<s:1> ntz空间都是L_p同构的。此外，存在一个关于上范数的m<s:1> ntz空间，它包含所有其他m<s:1> ntz空间作为补子空间。根据这个性质，这个空间是唯一的。考虑到这些结果，我们还想研究是否所有的超范数m<s:1> ntz空间都有Schauder基，我们想处理一个同构分类。对于C-Lambda空间也应处理类似的问题，C-Lambda空间可以粗略地看作是单位圆上的m<s:1> ntz空间的复类似物。最后，我们要处理四元数狄拉克模中的邵德基及相关问题。

I would like to invite Prof. Dr. Ludkovsky (Moskau) als guest for three months at the university of Paderborn. We want to continue our research on Müntz spaces and Banach spaces over quaternions. In particular, our three papers which we drafted so far shall be completed and submitted for publication. We show here that all Müntz spaces with respect to a reflexive L_p norm are isomorphic to l_p. Moreover there is a Müntz space with respect to the sup-norm which contains all other Müntz spaces as complemented subspaces. By this property this space is unique. Taking these results into account we also want to investigate whether all sup-norm Müntz spaces have a Schauder basis and we want to deal with an isomorphic classification. Similar questions shall be treated for C-Lambda spaces which can be roughly regarded as the complex analogues of Müntz spaces (over the unit circle). Finally we want to deal with Schauder bases in Dirac modules over quaternions and related questions.