Linear functionals and the duality principle for harmonic functions

Let H be the class of complex-valued harmonic functions in the unit disk < 1 and H1 the set of all functions such that f(0) = 0, fz (0) = 1 and f z (0) = For V its dual V* is where denotes the Hadamard product for harmonic functions. The set V is a dual class if V = W* for some W. In the present paper, the duality principle is extended to by means of the Hadamard product. Counterparts of the dual classes are introduced and their structural properties studied. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.