The Liouville theorem for $$p$$ p -harmonic functions and quasiminimizers with finite energy
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-020-02536-2
Abstract: We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite p th power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global… read more here.
Keywords: finite energy; harmonic functions; functions quasiminimizers; energy ... See more keywords
Asymptotic behavior of interpolation polynomials of harmonic functions based on radon projections
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DOI: 10.1007/s10092-017-0212-9
Abstract: We study the asymptotic behavior of harmonic interpolation of harmonic functions based on Radon projections when the chords coalesce to some points, a chord and a point. We show that the limit is the Lagrange… read more here.
Keywords: asymptotic behavior; based radon; harmonic functions; functions based ... See more keywords
Monopoles, Dipoles, and Harmonic Functions on Bratteli Diagrams
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DOI: 10.1007/s10440-018-0189-7
Abstract: In our study of electrical networks we develop two themes: finding explicit formulas for special classes of functions defined on the vertices of a transient network, namely monopoles, dipoles, and harmonic functions. Secondly, our interest… read more here.
Keywords: functions bratteli; harmonic functions; dipoles harmonic; monopoles dipoles ... See more keywords
A Schwarz Lemma for Harmonic Functions in the Real Unit Ball
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DOI: 10.1007/s10473-019-0512-z
Abstract: We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen’s Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping. read more here.
Keywords: harmonic functions; schwarz lemma; unit ball; functions real ... See more keywords
Harmonic Function with Correlated Coefficients
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DOI: 10.1007/s10473-019-0615-6
Abstract: In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri… read more here.
Keywords: function correlated; harmonic functions; correlated coefficients; harmonic function ... See more keywords
Boundary Integral Formula for Harmonic Functions on Riemann Surfaces
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DOI: 10.1007/s40315-020-00308-x
Abstract: We construct a boundary integral formula for harmonic functions on smoothly-bordered subdomains of Riemann surfaces embeddable into $${\mathbb {C}}{\mathbb {P}}^2$$ C P 2 . The formula may be considered as an analogue of the Green’s… read more here.
Keywords: harmonic functions; integral formula; formula; riemann surfaces ... See more keywords
Unitary representations of three dimensional Lie groups revisited: A short tutorial via harmonic functions
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DOI: 10.1016/j.geomphys.2017.01.004
Abstract: Abstract The representation theory of three dimensional real and complex Lie groups is reviewed from the perspective of harmonic functions defined over certain appropriate manifolds. An explicit construction of all unitary representations is given. The… read more here.
Keywords: three dimensional; harmonic functions; unitary representations; lie groups ... See more keywords
Ultradistributional boundary values of harmonic functions on the sphere
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.08.035
Abstract: Abstract We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their… read more here.
Keywords: harmonic functions; ultradistributional boundary; boundary values; functions sphere ... See more keywords
Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
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DOI: 10.1016/j.jmaa.2018.04.044
Abstract: Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several… read more here.
Keywords: harmonic functions; weakly conformal; generalized harmonic; horizontally weakly ... See more keywords
A boundary formula for reproducing kernel Hilbert spaces of real harmonic functions in Lipschitz domains
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DOI: 10.1080/17476933.2019.1709967
Abstract: This paper develops a new Hilbert space method to characterize a family of reproducing kernel Hilbert spaces of real harmonic functions in a bounded Lipschitz domain . Such method involves some families of positive self-adjoint… read more here.
Keywords: harmonic functions; reproducing kernel; hilbert spaces; spaces real ... See more keywords
Analogs of the Liouville Property for Harmonic Functions on Unbounded Domains
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DOI: 10.1134/s0037446620040035
Abstract: We obtain some analogs of the Liouville property for the function that is harmonic on the exterior of a Jordan domain $ G\subset{\mathbb{C}} $ and has constant boundary values of the function itself and its… read more here.
Keywords: liouville property; harmonic functions; property harmonic; analogs liouville ... See more keywords