Computational Methods and Function Theory 9 (2009), No. 1, 1--12
Copyright Heldermann Verlag 2009
Vangelis Stefanopoulos
vstefan@ucy.ac.cy , University of Cyprus, Department of Mathematics and Statistics, 1678 Nicosia, Cyprus.
We prove the existence of universal series whose terms are fundamental solutions, or derivatives of them, of the Cauchy-Riemann operator. By universal we mean a series whose partial sums are dense, with respect to the uniform topology on compacta, in the space of functions holomorphic on a certain subset of the complex plane. We show in particular that the coefficients of the series may be chosen to belong to some subspace of complex sequences like lp, 1≤p≤∞, or c0.
Keywords: Universal series, Cauchy-Riemann operator, fundamental solutions, zeta function.
MSC 2000: 30B10, 35E05, 30E10.
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