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Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions [PDF]
Abstract and Applied Analysis, 2012 For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians on M and N, we determine conditions under
M. T. Mustafa
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On Pairs of Harmonic Functions [PDF]
Proceedings of the American Mathematical Society, 1957 These relations imply that u and v are harmonic, but of course not all harmonic functions satisfy (1). It seems interesting to consider pairs of harmonic functions without the additional restrictions implied in (1), and see to what extent the conjugate character of u and v (over and above their harmonic character) enters into the results of classical ...
R. M. Redheffer
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Symmetry, Integrability and Geometry: Methods and Applications, 2007 Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory.
Shihshu Walter Wei
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Examples of harmonic functions [PDF]
Bulletin of the American Mathematical Society, 1932 Alfred J. Maria
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Harmonic series with polylogarithmic functions [PDF]
Vojnotehnički Glasnik, 2022 Introduction/purpose: Some sums of the polylogarithmic function associated with harmonic numbers are established. Methods: The approach is based on using the summation methods.
Vuk Stojiljković +2 more
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On s-harmonic functions on cones [PDF]
Analysis & PDE, 2018 37 pages, 3 ...
Terracini, Susanna +2 more
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Functionals of Harmonics Functions [PDF]
The First International Conference on Symmetry, 2018 Ministerio de Economía y ...
Quintero, Niurka R. +2 more
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Univalent harmonic functions [PDF]
Transactions of the American Mathematical Society, 1987 Several families of complex-valued, univalent, harmonic functions are studied from the point of view of geometric function theory. One class consists of mappings of a simply-connected domain onto an infinite horizontal strip with a normalization at the origin.
Glenn Schober, Walter Hengartner
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Axially Harmonic Functions and the Harmonic Functional Calculus on the S-spectrum
The Journal of Geometric Analysis, 2022 AbstractThe spectral theory on theS-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional heat diffusion and to the spectral theory for the Dirac operator on manifolds.
Colombo F. +3 more
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ON MULTIVALENT HARMONIC MEROMORPHIC FUNCTIONS INVOLVING HYPERGEOMETRIC FUNCTIONS [PDF]
المجلة العراقية للعلوم الاحصائية, 2011 In this paper we introduce a subclass of multivalent harmonic meromorphic functions defined in the exterior of the unit disk by using generalize hypergeometric functions.
ABDULRAHMAN SALMAN JUMA
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