2019/05/07 by Daghighi, Abtin, Gauthier, Paul M.
#30G30 #35G05 #46E25 #46J15 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1905.02514
The most important uniform algebra is the family of continuous functions on a compact subset K of the complex plane ℂ which are analytic on the interior int(K) For compact sets K which are regular (i.e. K =int(K) and for polyanalytic functions, we introduce analogous spaces, which are Banach spaces with respect to the sup-norm, but are not closed with respect to the usual pointwise multiplication. We shall introduce a multiplication on these spaces and investigate the resulting algebras.