On the Approximation and Growth of Entire Harmonic Functions in ℝn

Veselovska, Olga

doi:10.1007/s11253-018-1514-z

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2023

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Cited by 3 publications

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“…The reverse inequality in (20) holds immediately by applying Lemma 1 of [14]. This completes the proof of Theorem 5.…”

Section: Resultssupporting

confidence: 60%

“…The reverse inequality in (13) can be obtained immediately by using Lemma 1 of [14]. Hence the proof is completed.…”

Section: Resultsmentioning

confidence: 78%

“…Veselovska [14] established conditions under which a harmonic function in B n R (a ball of radius R in n-dimensional space R n ) continues to the entire harmonic function and derived formulae for the generalized growth characteristics. It has been noticed that these characteristics have not studied so extensively in non-entire case in comparison to entire case.…”

Section: Introductionmentioning

confidence: 99%

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GENERALIZED GROWTH AND APPROXIMATION OF HARMONIC FUNCTIONS IN ${R}^{n}, n\ge 3$

Kumar¹,

Vishnoi²

2022

Int. J. of Appl. Math.

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“…The reverse inequality in (20) holds immediately by applying Lemma 1 of [14]. This completes the proof of Theorem 5.…”

Section: Resultssupporting

confidence: 60%

“…The reverse inequality in (13) can be obtained immediately by using Lemma 1 of [14]. Hence the proof is completed.…”

Section: Resultsmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

GENERALIZED GROWTH AND APPROXIMATION OF HARMONIC FUNCTIONS IN ${R}^{n}, n\ge 3$

Kumar¹,

Vishnoi²

2022

Int. J. of Appl. Math.

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Generalized growth and weighted polynomial approximation of entire function solutions of certain elliptic partial differential equation

Kumar,

Basu

2023

J Anal

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On the Approximation of Entire Harmonic Functions in ℝⁿ Having Slow Growth

Kumar¹,

Ghareeb

2022

Journal of Mathematics

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The generalized growth of entire transcendental functions in terms of polynomial approximation errors in some Banach spaces has been studied by various authors. The main purpose of this paper is to study the harmonic polynomial approximation of entire harmonic functions in space ℝ n , n ≥ 3 , in certain Banach spaces. Moreover, the generalized type of harmonic functions of slow growth has been characterized in terms of best harmonic polynomial approximation errors. Our results add new aspects for the case of order zero.

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On the Approximation and Growth of Entire Harmonic Functions in ℝn

Cited by 3 publications

References 1 publication

GENERALIZED GROWTH AND APPROXIMATION OF HARMONIC FUNCTIONS IN ${R}^{n}, n\ge 3$

GENERALIZED GROWTH AND APPROXIMATION OF HARMONIC FUNCTIONS IN ${R}^{n}, n\ge 3$

Generalized growth and weighted polynomial approximation of entire function solutions of certain elliptic partial differential equation

On the Approximation of Entire Harmonic Functions in ℝⁿ Having Slow Growth

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On the Approximation and Growth of Entire Harmonic Functions in ℝn

Cited by 3 publications

References 1 publication

GENERALIZED GROWTH AND APPROXIMATION OF HARMONIC FUNCTIONS IN ${R}^{n}, n\ge 3$

GENERALIZED GROWTH AND APPROXIMATION OF HARMONIC FUNCTIONS IN ${R}^{n}, n\ge 3$

Generalized growth and weighted polynomial approximation of entire function solutions of certain elliptic partial differential equation

On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth

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On the Approximation of Entire Harmonic Functions in ℝⁿ Having Slow Growth