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Generalized growth of special monogenic functions having finite convergence radius. (English) Zbl 1483.30091

Summary: In the present paper, we study the growth of special monogenic functions having finite convergence radius. The characterizations of generalized order and generalized type of special monogenic functions having finite convergence radius have been obtained in terms of their Taylor’s series coefficients.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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References:

[1] D. Constales, R.De. Almeida, R.S. Krausshar, On the growth type of entire monogenic functions, Arch. Math. 88 (2007) 153-163. · Zbl 1109.30040
[2] D. Constales, R.De. Almeida, R.S. Krausshar, On the relation between the growth and the Taylor coefficients of entire solutions to the higher dimensional CauchyRiemann system inRn+1,J. Math. Anal. App. 327 (2007) 763-775. · Zbl 1108.30041
[3] R.De. Almeida, R.S. Krausshar, On the asymptotic growth of entire monogenic functions, Z. Anal. Anwendungen 24 (2005) 791-813. · Zbl 1095.30044
[4] G.S. Srivastava, S. Kumar, On the generalized order and generalized type of entire monogenic functions, Demon. Math. 46 (2013) 663-677. · Zbl 1290.30062
[5] M.A. Abul-Ez, D. Constales, Linear substitution for basic sets of polynomials in Clifford analysis, Portugaliae Math. 48 (1991) 143-154. · Zbl 0737.30029
[6] M.A. Abul-Ez, R.De. Almeida, On the lower order and type of entire axially monogenic function, Results Math. 63 (2013) 1257-1275. · Zbl 1270.30017
[7] S. Kumar, Generalized growth of special monogenic functions, Journal of Complex Analysis 2014 (2014) 1-5. · Zbl 1310.30041
[8] D. Constales, R.De. Almeida, R.S. Krausshar, Basics of generalized Wiman - Valiron theory for monogenic Taylor series of finite convergence radius, Math. Z. 266 (2010) 665-681. · Zbl 1208.30044
[9] S. Kumar, K. Bala, Generalized growth of monogenic Taylor series of finite convergence radius, Ann. Univ. Ferrara 59 (2013) 127-140. · Zbl 1300.30091
[10] M.A. Abul-Ez, D. Constales, Basic sets of polynomials in Clifford analysis, Complex Var. Theory Appl. 14 (1990) 177-185. · Zbl 0663.41009
[11] M.N. Seremeta, On the connection between the growth of a function analytic in a disc and modulie of its Taylor series, Visnik L’viv Derzh Univ. Ser. Mekh. Mat. 2 (1965) 101-110.
[12] S. Kumar, K. Bala, Generalized order of entire monogenic functions of slow growth, J. Nonlinear Sci. App. 5 (2012) 418-425. · Zbl 1295.30114
[13] S. Kumar, K. Bala, Generalized type of entire monogenic functions of slow growth, Trans. Journal Math. Mech. 3 (2011) 95-102. · Zbl 1273.30044
[14] G.S. Srivastava, S. Kumar, On approximation and generalized type of analytic functions of several complex variables, Anal. Theory Appl. 27 (2011) 101-108. · Zbl 1249.32015
[15] G.S. Srivastava, S. Kumar, Generalized growth of solutions to a class of elliptic partial differential equations, Acta Mathematica Vietnamica 37 (2012) 11-21 · Zbl 1291.30015
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