Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\)

Devendra Kumar

doi:10.33993/jnaat472-1166

Authors

Devendra Kumar M.M.H.College, India

DOI:

https://doi.org/10.33993/jnaat472-1166

Keywords:

approximation errors, entire harmonic functions, generalized order, generalized type, ball of radius r

Abstract views: 279

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.

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