On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth
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 ℝn, n≥3, in certain...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7420942 |
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| _version_ | 1832563865715474432 |
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| author | Devendra Kumar A. Ghareeb |
| author_facet | Devendra Kumar A. Ghareeb |
| author_sort | Devendra Kumar |
| collection | DOAJ |
| description | 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 ℝn, 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. |
| format | Article |
| id | doaj-art-c2b837d03890428e966999b9fa0b57c5 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c2b837d03890428e966999b9fa0b57c52025-02-03T01:12:21ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7420942On the Approximation of Entire Harmonic Functions in ℝn Having Slow GrowthDevendra Kumar0A. Ghareeb1Department of MathematicsDepartment of MathematicsThe 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 ℝn, 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.http://dx.doi.org/10.1155/2022/7420942 |
| spellingShingle | Devendra Kumar A. Ghareeb On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth Journal of Mathematics |
| title | On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth |
| title_full | On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth |
| title_fullStr | On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth |
| title_full_unstemmed | On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth |
| title_short | On the Approximation of Entire Harmonic Functions in ℝn Having Slow Growth |
| title_sort | on the approximation of entire harmonic functions in rn having slow growth |
| url | http://dx.doi.org/10.1155/2022/7420942 |
| work_keys_str_mv | AT devendrakumar ontheapproximationofentireharmonicfunctionsinrnhavingslowgrowth AT aghareeb ontheapproximationofentireharmonicfunctionsinrnhavingslowgrowth |