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

全纯、调和和实解析函数的特殊 Banach 空间的研究

• 批准号: 256279602
• 负责人: Professor Dr. Wolfgang Lusky
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/256279602?language=en
• 关键词: Investigation; special; Banach; spaces; holomorphic

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.

我想邀请卢德科夫斯基教授（莫斯科）到帕德博恩大学做客三个月。我们想继续研究四元数上的Müntz空间和Banach空间。特别是，我们迄今起草的三份文件将完成并提交出版。本文证明了所有关于自反L_p范数的Müntz空间都同构于L_p，并且存在一个关于超范数的Müntz空间，它包含所有其它的Müntz空间作为补子空间.这个空间是独一无二的。考虑到这些结果，我们还想研究是否所有的超范数Müntz空间都有一个Schauder基，我们想处理一个同构分类。对于C-Lambda空间，类似的问题也应该被处理，C-Lambda空间可以被粗略地看作是Müntz空间（在单位圆上）的复类似物。最后，我们要处理Schauder基狄拉克模在四元数和相关问题。