Harnack inequalities for Schrödinger operators
Wolfhard Hansen (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “Harmonic functions on annuli of graphs”
Harnack inequalities for Schrödinger operators
On the graphs with maximum distance or -diameter
Wayne Goddard, Christine S. Swart, Henda C. Swart (2005)
Mathematica Slovaca
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The Path-Distance-Width of Hypercubes
Yota Otachi (2013)
Discussiones Mathematicae Graph Theory
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The path-distance-width of a connected graph G is the minimum integer w satisfying that there is a nonempty subset of S ⊆ V (G) such that the number of the vertices with distance i from S is at most w for any nonnegative integer i. In this note, we determine the path-distance-width of hypercubes.
On the axiomatic of harmonic functions I
Corneliu Constantinescu, A. Cornea (1963)
Annales de l'institut Fourier
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On présente quelques remarques sur l’axiomatique des fonctions harmoniques de M. Brelot. Ainsi, on montre qu’il est possible de remplacer dans l’axiome 3 l’ensemble ordonné filtrant des fonctions harmoniques par une suite monotone, et, s’il existe une fonction surharmonique positive alors : a) l’espace est la réunion d’un fermé polaire et d’un ouvert -compact ; b) l’espace possède une base dénombrable s’il est localement à base dénombrable ; c) l’ensemble des composants...
Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces
Philippe Jaming (1999)
Colloquium Mathematicae
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We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball . We then study the Hardy spaces , 0
-harmonic measure is not additive on null sets
José G. Llorente, Juan J. Manfredi, Jang-Mei Wu (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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When and the -harmonic measure on the boundary of the half plane is not additive on null sets. In fact, there are finitely many sets , ,..., in , of -harmonic measure zero, such that .