On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces

摘要

For the entire transcendental functions f of many complex variables m (m a parts per thousand yen 2) of finite generalized order of growth rho (m) (f; alpha, beta), we obtain the limiting relations between the indicated characteristic of growth and the sequences of best polynomial approximations of f in the Hardy Banach spaces H (q) (U (m) ) and in the Banach spaces Bm(p, q, a ) studied by Gvaradze. The presented results are extensions of the corresponding assertions made by Varga, Batyrev, Shah, Reddy, Ibragimov, and Shikhaliev to the multidimensional case.