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On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation

Kumar Devendra, Alghamdi Azza M.

Demonstratio Mathematica

2022

Vol. 55, nr 1

429--436

For an entire function solution of generalized bi-axisymmetric potential equation, we obtain a relationship between the generalized growth characteristics and polynomial approximation errors in sup norm by using the general functions introduced by Seremeta [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. 88 (1970), no. 2, 291–301].

Approximation of entire transcendental functions of several complex variables in some Banach spaces for slow growth

Kumar D.

Journal of Applied Analysis

2017

Vol. 23, nr 1

9--20

In the present paper, the coefficients characterizations of generalized type Tm(f; α, α) of entire transcendental functions f of several complex variables m (m ≥ 2) for slow growth have been obtained in terms of the sequence of best polynomial approximations of f in the Hardy Banach spaces Hq(Um) and in the Banach spaces Bm(p, q, λ). The presented work is the extension and refinement of the corresponding assertions made by Vakarchuk and Zhir [20-25], Gol’dberg [4] and Sheremeta [17, 18] to the multidimensional case.

On the generalized order and generalized type of entire monogenic functions

Srivastava G. S., Kumar S.

Demonstratio Mathematica

2013

Vol. 46, nr 4

663--677

In the present paper we study the generalized growth of entire monogenic functions. The generalized order, generalized lower order and generalized type of entire monogenic functions have been obtained in terms of its Taylor’s series coefficients.

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

Kumar D.

Journal of Applied Analysis

2012

Vol. 18, nr 2

179-196

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.

Generalized growth of entire harmonic functions

Srivastava G. S.

Fasciculi Mathematici

2008

Nr 40

79-89

Let H(x), x = (x1, x2, ... , xn), be an entire harmonic function in Rn.Fryant and Shankar [1] had obtained growth properties of H explicitly in terms of its Fourier coeffcients. In this paper, we obtain the characterizations of generalized order and type and introduce the generalized lower order for H. Special case of functions of slow growth has also been considered. Our results generalize some of the results obtained in [1].