Approximation of entire function solutions of the Helmholtz equation having slow growth

• Autorzy: Kumar D.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the Chebyshev polynomial approximation of entire solutions of Helmholtz equations in R2 in Banach spaces (B(p, q, m) space, Hardy space and Bergman space). Some bounds on generalized order of entire solutions of Helmholtz equations of slow growth have been obtained in terms of the coefficients and approximation errors using function theoretic methods.

Słowa kluczowe

EN

generalized order; entire function; Helmholtz equation; Chebyshev approximation error

PL

funkcja całkowita; równanie Helmholtza; wielomiany Czebyszewa

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2012
• Tom: Vol. 18, nr 2
• Strony: 179--196
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kumar D.

• Department of Mathematics, M. M. H.College, Model Town, Ghaziabad 201001 U.P., India,

Bibliografia

• [1] S. Bergman, Integral Operators in the Theory of Linear Partial Differential Equations, Ergeb. Math. Grenzgeb. 23, Springer, New York, 1969.
• [2] R. P. Gilbert, Function Theoretic Methods in Partial Differential Equations, Math. Sci. Eng. 54, Academic Press, New York, 1969.
• [3] R. P. Gilbert and D. L. Colton, Integral operator methods in biaxially symmetric potential theory, Contrib. Differential Equations 2 (1963), 441-156.
• [4] R. P. Gilbert and D. L. Colton, Singularities of solutions to elliptic partial differential equations, Quarterly J. Math. 19 (1968), 391-396.
• [5] M.I. Gvaredze, On the class of spaces of analytic functions, Mat. Zametki 21(1994), 141-150.
• [6] G. P. Kapoor and A. Nautiyal, Polynomial approximation of an entire function of slow growth, J. Approx. Theory 32 (1981), 64-75.
• [7] E. O. Kreyszig and M. Kracht, Methods of Complex Analysis in Partial Differential Equations with Applications, Can. Math. Soc. Ser. Monogr. Adv. Texts, John Wiley and Sons, New York, 1988.
• [8] P. A. McCoy, Polynomial approximation and growth of generalized axisymmetric potentials, Canadian J. Math. 31 (1979), 49-59.
• [9] P. A. McCoy, Solution of the Helmholtz equation having rapid growth, Complex Var. Elliptic Equ. 18 (1992), 91-101.
• [10] A. Nautiyal, On the growth of entire solutions of generalized axially symmetric Helmholtz equation, Indian J. Pure Appl. Math. 14 (1983), 718-721.
• [11] A. R. Reddy, Best approximation of certain entire functions, J. Approx. Theory 5 (1972), 97-112.
• [12] M.N. Seremeta, On the connection between the growth of order zero of entire or analytic functions in a circle and the coefficients of their power expansions (in Rusian), Izvestiya Vuzov, Mathematica 6 (1968), 115-121.
• [13] M. N. Seremeta, On the connection between the growth of the maximum modules of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. 88 (1970), 291-301.
• [14] S. B. Vakarchuk, On the best polynomial approximation in some Banach spaces for functions analytic in the unit disc, Math. Notes 55 (1994), 338-343.
• [15] S. B. Vakarchuk and S. I. Zhir, On polynomial approximation of entire transcendental functions (in Russian), Mathematicheskaya Fizika Analys Geometriya 9 (2002), 595-603.
• [16] S. B. Vakarchuk and S. I. Zhir, On some problems of polynomial approximation of entire transcendental functions, Ukrainian Math. J. 54 (2002), 1393-1401.