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In the present paper, the coefficients characterizations of generalized typeT  m   ⁢   (  f  ;  α  ,  α  ){T_{m}(f;\alpha,\alpha)}    of entire transcendental functions  f  of several complex variables  m  (m  ≥  2  ){m\geq 2)}    for slow growth have been obtained in terms of the sequence of best polynomial approximations of  f  in the Hardy Banach spacesH  q   ⁢   (   U  m   ){H_{q}(U^{m})}    and in the Banach spacesB  m   ⁢   (  p  ,  q  ,  λ  ){B_{m}(p,q,\lambda)}   . The presented work is the extension and refinement of the corresponding assertions made by Vakarchuk and Zhir [ 22 ,  20 ,  21 ,  23 ,  24 ,  25 ], Gol’dberg [ 4 ] and Sheremeta [ 17 ,  18 ] to the multidimensional case.

Approximation of entire transcendental functions of several complex variables in some Banach spaces for slow growth