On the fast growth of analytic functions by means of Lagrange polynomial approximation and interpolation in C^N*

• Autorzy: Kumar D.
• Języki publikacji: EN

Abstrakty

EN

The present paper is concerned with the fast growth of analytic functions in the sets of the form ...[wzór] is the Siciak extremal function of a compact set K) by means of the Lagrange polynomial approximation and interpolation on K having rapidly increasing maximum modulus. To study the precise rates of growth of such functions the concept of index has been used.

Słowa kluczowe

EN

index-q; approximation and interpolation; fast growth and analytic functions

PL

aproksymacja funkcji; interpolacja funkcji; funkcja analityczna

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 43
• Strony: 85--99
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Kumar D.

• Department of Mathematics Research and Post Graduate Studies M.M.H. College, Model Town, Ghaziabad, U.P., India,

Bibliografia

• [1] Beuermann F., Wachstumsordnung, Koeffizientenwachstum and Nullstellendichte bei Potenzreichenmit endlichen Konvergenzkreis, Math. Zeit., 33(1931), 98-108.
• [2] Juneja O.P., Kapoor G.P., Bajpai S.K., On the (p, q)−order and lower (p, q)−order of an entire function, J. Reine Angew. Math., 282(1976), 53-67.
• [3] Juneja O.P., Kapoor G.P., Bajpai S.K., On the (p, q)−type and lower (p, q)−type of an entire function, J. Reine Angew. Math., 290(1977), 180-190.
• [4] Juneja O.P., Kapoor G.P., Analytic Functions-Growth Aspects, Research Notes in Mathematics,104,Pitman Advanced Publishing Program, Boston, London and Melbourne, 1985.
• [5] Muller J., Accelerated polynomial approximation of finite order entire functions by growth reduction, Mathematics of Computation 66, 218(1997), 743-761.
• [6] Kapoor G.P., Nautiyal A., Polynomial approximation of an entire function of slow growth, J. Approx. Theory, 32(1981), 64-75.
• [7] Kapoor G.P., Nautiyal A., Approximation of entire functions over Caratheodory domains, Bull. Austral. Math. Soc., 25(1982), 221-229.
• [8] Kasana H.S., Kumar D., On approximation and interpolation of entire functions with index-pair (p, q), Publicacion Matematiques, 38(1994), 255-267.
• [9] Kasana H.S., Kumar D., On polynomial approximation of entire functions with index-pair (p, q), Rend. Istit. Mat. Univ. Trieste, 35(2003), 49-59.
• [10] Kumar D., On approximation and interpolation of entire functions in two complex variables with index-pair (p, q), Commun. Fac. Sci. Univ. Ank. Series A1, 51(2)(2002), 47-56.
• [11] Massa S., Remarks on the growth of entire function and the degree of approximation, Riv. Mat. Univ. Parma, 7(4)(1981), 1-6.
• [12] Nautiyal A., Rizvi S.R.H., On the approximation of an entire function in Lα−norm, J. Indian Acad. Math., 1(4)(1982), 16-20.
• [13] Nautiyal A., Rizvi S.R.H., Kapoor G.P., On the approximation of an entire function in L2−norm, Bull. Malaysian Math. Soc., 2(5)(1982),21-31.
• [14] Reddy A.R., A contribution to best approximation in the L2−norm, J. Approx. Theory, 11(1974), 110-117.
• [15] Reddy A.R., Best polynomial approximation to certain entire functions, J. Approx. Theory, 5(1972), 97-112.
• [16] Rice J.R., The degree of convergence for entire functions, Duke Math. J., 38(1971), 429-440.
• [17] Rizvi S.R.H., Interpolation series and approximation of entire functions, The Math. Student, 50(1982), 50-57.
• [18] Rizvi S.R.H., Juneja O.P., A contribution to best approximation in the L2−norm, Publications De L’Institute Mathematique, 42(28)(1980), 167-177.
• [19] Shah S.M., Polynomial approximation of an entire function and generalized orders, J. Approx. Theory, 19(1977), 315-324.
• [20] Siciak J., On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc., 105(1962), 322-357.
• [21] Siciak J., Extremal plurisubharmonic functions in CN, Proceedings of the First Finnish-Polish Summer School in Complex Analysis at Podlesice (Lodz 1977), Univ. of Lodz, 115-152.
• [22] Stall W., Holomorphic Functions of Finite Order in Several Complex Variables, Providence, R.I. 1974.
• [23] Winiarski T., Approximation and interpolation of entire functions, Ann. Polon. Math., 29(1970), 259-273.
• [24] 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.