Generalized Lower Order and Approximation of Entire Transcendental Functions of Several Complex Variables in Some Banach Spaces

We obtain coefficients characterizations of generalized lower order lambda(m)(f, alpha, beta) of entire transcendental functions f of m several complex variables m >= 2 for generalized growth in terms of the sequence of best polynomial approximations of f in the Hardy Banach spaces H-q(U-m) and in the Banach spaces B-m(p, q, eta). The presented results are extensions of investigations made by Vakarchuk and Zhir [17-21] and by Goldberg and Shah [4,13] to the multidimensional case.