Density of polynomials in classes of functions on products of planar domains

摘要

For planar domains Omega(i), i is an element of I, where I is an arbitrary set, we give sufficient conditions for the density of polynomials in A(Pi(i is an element of I), Omega(i)) as well as in A(infinity) (Pi(i is an element of I), Omega(i)), endowed with their natural topologies. We also characterize the uniform limits with respect to the chordal metric, of polynomials on (i is an element of I), (Omega) over bar (i) Moreover, we discuss sets of uniqueness. (C) 2015 Elsevier Inc. All rights reserved.