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Displaying similar documents to “Topological countability in Brelot potential theory”

Some properties of the balayage of measures on a harmonic space

Corneliu Constantinescu (1967)

Annales de l'institut Fourier

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On démontre plusieurs théorèmes concernant le balayage des mesures sur un espace harmonique satisfaisant aux axiomes de Bauer, parmi lesquels nous indiquons les suivants : a) la balayée μ A B d’une mesure μ sur la réunion μ A μ B (dans l’espace de Riesz de mesure) ; b) ϵ x A ϵ x caractérise l’effilement de A en x  ; c) il existe un potentiel fini et continue p tel que pour tout ensemble A { x | R ^ p ( x ) < p ( x ) } est exactement l’ensemble des points où A est effilé ; d) μ A est portée par la fermeture fine de A  ; e) si A et B sont...

Uniform bounds for quotients of Green functions on C 1 , 1 -domains

H. Hueber, M. Sieveking (1982)

Annales de l'institut Fourier

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Let Δ u = Σ i 2 x i 2 , L u = Σ i , j a i j 2 x i x j u + Σ i b i x i u + c u be elliptic operators with Hölder continuous coefficients on a bounded domain Ω R n of class C 1 , 1 . There is a constant c > 0 depending only on the Hölder norms of the coefficients of L and its constant of ellipticity such that c - 1 G Δ Ω G L Ω c G Δ Ω on Ω × Ω , where γ Δ Ω (resp. G L Ω ) are the Green functions of Δ (resp. L ) on Ω .

A class of functions containing polyharmonic functions in ℝⁿ

V. Anandam, M. Damlakhi (2003)

Annales Polonici Mathematici

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Some properties of the functions of the form v ( x ) = i = 0 m | x | i h i ( x ) in ℝⁿ, n ≥ 2, where each h i is a harmonic function defined outside a compact set, are obtained using the harmonic measures.

On the integral representation of finely superharmonic functions

Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri (2019)

Commentationes Mathematicae Universitatis Carolinae

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In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset U of a Brelot 𝒫 -harmonic space Ω with countable base of open subsets and satisfying the axiom D . When Ω satisfies the hypothesis of uniqueness, we define the Martin boundary of U and the Martin kernel K and we obtain the integral representation of invariant functions by using the kernel K . As an application of the integral representation we extend to the cone...

Landau's theorem for p-harmonic mappings in several variables

Sh. Chen, S. Ponnusamy, X. Wang (2012)

Annales Polonici Mathematici

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A 2p-times continuously differentiable complex-valued function f = u + iv in a domain D ⊆ ℂ is p-harmonic if f satisfies the p-harmonic equation Δ p f = 0 , where p (≥ 1) is a positive integer and Δ represents the complex Laplacian operator. If Ω ⊂ ℂⁿ is a domain, then a function f : Ω m is said to be p-harmonic in Ω if each component function f i (i∈ 1,...,m) of f = ( f , . . . , f m ) is p-harmonic with respect to each variable separately. In this paper, we prove Landau and Bloch’s theorem for a class of p-harmonic mappings...

A poset of topologies on the set of real numbers

Vitalij A. Chatyrko, Yasunao Hattori (2013)

Commentationes Mathematicae Universitatis Carolinae

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On the set of real numbers we consider a poset 𝒫 τ ( ) (by inclusion) of topologies τ ( A ) , where A , such that A 1 A 2 iff τ ( A 1 ) τ ( A 2 ) . The poset has the minimal element τ ( ) , the Euclidean topology, and the maximal element τ ( ) , the Sorgenfrey topology. We are interested when two topologies τ 1 and τ 2 (especially, for τ 2 = τ ( ) ) from the poset define homeomorphic spaces ( , τ 1 ) and ( , τ 2 ) . In particular, we prove that for a closed subset A of the space ( , τ ( A ) ) is homeomorphic to the Sorgenfrey line ( , τ ( ) ) iff A is countable. We study also common...

On Ditkin sets

T. Muraleedharan, K. Parthasarathy (1996)

Colloquium Mathematicae

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In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter’s terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3])...

Axiomatic theory of harmonic functions. Balayage

Nicu Boboc, Corneliu Constantinescu, A. Cornea (1965)

Annales de l'institut Fourier

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Dans une axiomatique des fonctions harmoniques un peu plus générale que celle de H. Bauer, on démontre les relations suivantes : R s + t A = R s A + R t A , R s A B + R s A B R s A + R s B , A n A , S n s R s n A n R s A , A , B , A n , (resp. s , t , s n ) sont des ensembles (resp. fonctions hyperharmoniques non-négatives) arbitraires. Les mêmes relations sont valables pour R ^ . On démontre aussi que la relation * s d μ A = * R ^ s A d μ a lieu si l’espace de base a une base dénombrable ou si l’axiome D de M. Brelot est satisfait,...