Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Abtin Daghighi
Pages: [19] - [45]
Received Date: January 25, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_07100121763
We generalize to infinite dimensions the concept of polyanalytic functions. These are our main results: (1) A characterization based upon restriction, which generalizes a known characterization of holomorphic functions on Banach spaces. (2) A property of special local uniform limits which yields an approximation result. (3) We introduce meta-analytic functions on Hilbert manifolds together with a characterization compatible with (1). We also point out several corollaries to our characterizations.
infinite dimensional holomorphy, polyanalytic functions on Banach manifolds, meta-analytic functions.
