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

• Applicant: Professor Dr. Wolfgang Lusky
• Subject Area: Mathematics
• Term: from 2014 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 256279602

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.

• DFG Programme: Research Grants