Academic Journal
Permissible growth rates for Birkhoff type universal harmonic functions
| Τίτλος: | Permissible growth rates for Birkhoff type universal harmonic functions |
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| Συγγραφείς: | Armitage, David |
| Πηγή: | Journal of Approximation Theory. 136:230-243 |
| Στοιχεία εκδότη: | Elsevier BV, 2005. |
| Έτος έκδοσης: | 2005 |
| Θεματικοί όροι: | Translation, Mathematics(all), Numerical Analysis, Applied Mathematics, name=Analysis, Harmonic, Density, name=Applied Mathematics, Special classes of entire functions of one complex variable and growth estimates, Growth, name=Numerical Analysis, 01 natural sciences, Harmonic, subharmonic, superharmonic functions in higher dimensions, name=General Mathematics, harmonic function, universal function, growth rate, 0101 mathematics, Universal, Analysis |
| Περιγραφή: | A harmonic function \(H\) on \(\mathbb{R}^{n}\) \((n\geq 2)\) is called universal (in the sense of Birkhoff) if its set of translates \(\{x\mapsto H(a+x):a\in \mathbb{R}^{n}\}\) is dense in the space \(\mathcal{H}_{n}\) of all harmonic functions on \(\mathbb{R}^{n}\), endowed with the topology of local uniform convergence. The main result of this paper shows that universal harmonic functions may have arbitrarily prescribed growth. A result of this nature for holomorphic functions had previously been established by \textit{S. M. Duyos Ruis} [Dokl. Akad. Nauk SSSR 279, 792--795 (1984; Zbl 0599.30059)]. The author contrasts this behaviour with that of MacLane-type universal harmonic functions, the partial derivatives (rather than translates) of which are dense in \(\mathcal{H}_{n}\). Such functions do have a minimum growth rate: see \textit{M. P. Aldred} and \textit{D. H. Armitage} [J. Lond. Math. Soc. (2) 57, 148--156 (1998; Zbl 0922.31004)]. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 0021-9045 |
| DOI: | 10.1016/j.jat.2005.07.006 |
| Σύνδεσμος πρόσβασης: | https://dblp.uni-trier.de/db/journals/jat/jat136.html#Armitage05 https://pure.qub.ac.uk/portal/en/publications/permissible-growth-rates-for-birkhoff-type-universal-harmonic-functions(eebc45e3-9644-4cf6-9aa3-49eab3b33d0c).html https://dialnet.unirioja.es/servlet/articulo?codigo=1276620 https://pure.qub.ac.uk/en/publications/permissible-growth-rates-for-birkhoff-type-universal-harmonic-fun https://core.ac.uk/display/82279755 https://www.sciencedirect.com/science/article/pii/S0021904505001383 |
| Rights: | Elsevier Non-Commercial |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....51e9ec91ff7eedb9a2c2d30af68f8a17 |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 00219045 |
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| DOI: | 10.1016/j.jat.2005.07.006 |