Abstract
In this paper we study the continuation of harmonic functions in the ball to the entire harmonic functions in space \(\mathbb{R}^n\), \(n\geq 3\).
The generalized order introduced by M.N. Seremeta has been used to characterize the growth of such functions. Moreover, the generalized order, generalized lower order and generalized type have been characterized in terms of harmonic polynomial approximation errors.
Our results apply satisfactorily for slow growth.
Publisher
Academia Romana Filiala Cluj
Reference15 articles.
1. A.V. Batyrev, On the problem of best approximation of an analytic function by polynomials, Dokl. Akad. Nauk. SSR [Soviet Math. Dokl.], 26 (1951), pp. 173–175.
2. A. Giroux, Approximation of entire functions over bounded domains, J. Approx. Theory, 28 (1980), pp. 45–53 https://doi.org/10.1016/0021-9045(80)90103-3
3. I.I. Ibragimov, N. Shikhaliev, On the best mean approximation of analytic functions in the space Lp, Trudy Inst. Mat. Mekh. Azreb. SSR, pp. 84–86 (1977).
4. N. Juhong, C. Qing, Approximation of entire functions of slow growth, Intern. J. Pure and Appl. Math. 113 (2017) no.3, pp. 399–413.
5. G.P. Kapoor, A. Nautiyal, Polynomial approximation of an entire function of slow growth, J. Approx. Theory, 32 (1981), pp. 64–75, https://doi.org/10.1016/0021-9045(81)90022-8