Previous |  Up |  Next


entire function; Siciak extremal function; generalized order; generalized type; approximation errors; interpolation errors
In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
[1] Ganti, R., Srivastava, G. S.: Approximation of entire functions of slow growth. General Math. 14 (2) (2006), 65–82. MR 2270298 | Zbl 1164.30301
[2] Janik, A.: A characterization of the growth of analytic functions by means of polynomial approximation. Univ. Iagel. Acta Math. 24 (1984), 295–319. MR 0815914 | Zbl 0554.32015
[3] Janik, A.: On approximation of entire functions and generalized order. Univ. Iagel. Acta Math. 24 (1984), 321–326. MR 0815915
[4] Kapoor, G. P., Nautiyal, A.: Polynomial approximation of an entire function of slow growth. J. Approx. Theory 32 (1981), 64–75. DOI 10.1016/0021-9045(81)90022-8 | MR 0629582 | Zbl 0495.41005
[5] Seremeta, M. N.: On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion. Amer. Math. Soc. Transl. Ser. 2 88 (1970), 291–301.
[6] Shah, S. M.: Polynomial approximation of an entire function and generalized order. J. Approx. Theory 19 (1977), 315–324. DOI 10.1016/0021-9045(77)90095-8 | MR 0440254
[7] Winiarski, T.: Application of approximation and interpolation methods to the examination of entire functions of $n$ complex variables. Ann. Polon. Math. 28 (1973), 97–121. MR 0328091 | Zbl 0257.32008
Partner of
EuDML logo