×

Polynomial approximation and interpolation of entire functions of slow growth in several complex variables. (English) Zbl 1312.32005

Summary: In the present paper, a characterization of the generalized order and type of entire functions of several complex variables by means of polynomial approximation and interpolation have been obtained. Our results improve and generalize various results of S. M. Shah [J. Approximation Theory 19, 315–324 (1977; Zbl 0311.30034)], M. N. Seremeta [Am. Math. Soc., Transl., II. Ser. 88, 291–301 (1970); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1967, No. 2 (57), 100–108 (1967; Zbl 0198.10803)], G. P. Kapoor and A. Nautiyal [J. Approximation Theory 32, 64–75 (1981; Zbl 0495.41005)], S. B. Vakarchuk [Math. Notes 55, No. 4, 338–343 (1994); translation from Mat. Zametki 55, No. 4, 6–14 (1994; Zbl 0822.41006)], S. B. Vakarchuk and S. I. Zhir [Ukr. Math. J. 54, No. 9, 1393–1401 (2002); translation from Ukr. Mat. Zh. 54, No. 9, 1155–1162 (2002; Zbl 1020.30042)], T. Winiarski [Ann. Pol. Math. 28, 97–121 (1973; Zbl 0257.32008); Ann. Pol. Math. 23, 259–273 (1970; Zbl 0205.37905)]. In this way, we summarize and unify the work which has been done on this subject to-date.

MSC:

32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
41A10 Approximation by polynomials