Displaying similar documents to “Uniform approximation of continuous functions on compact sets by biharmonic functions”

Biharmonic morphisms

Mustapha Chadli, Mohamed El Kadiri, Sabah Haddad (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let ( X , ℋ ) and ( X ' , ℋ ' ) be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from ( X , ℋ ) to ( X ' , ℋ ' ) is a continuous map from X to X ' which preserves the biharmonic structures of X and X ' . In the present work we study this notion and characterize in some cases the biharmonic morphisms between X and X ' in terms of harmonic morphisms between the harmonic spaces associated with ( X , ℋ ) and ( X ' , ℋ ' ) and the coupling kernels of them.

"Counterexamples" to the harmonic Liouville theorem and harmonic functions with zero nontangential limits

A. Bonilla (2000)

Colloquium Mathematicae

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We prove that, if μ>0, then there exists a linear manifold M of harmonic functions in ℝ N which is dense in the space of all harmonic functions in ℝ N and lim‖x‖→∞ x ∈ S ‖x‖μDαv(x) = 0 for every v ∈ M and multi-index α, where S denotes any hyperplane strip. Moreover, every nonnull function in M is universal. In particular, if μ ≥ N+1, then every function v ∈ M satisfies ∫H vdλ =0 for every (N-1)-dimensional hyperplane H, where λ denotes the (N-1)-dimensional Lebesgue measure. On the other...

On the axiomatic of harmonic functions II

Corneliu Constantinescu, A. Cornea (1963)

Annales de l'institut Fourier

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On démontre dans l’axiomatique de M. Brelot la linéarité de l’opération de balayage appliquée aux fonctions surharmoniques en utilisant seulement les axiomes 1, 2, 3, l’espace de base n’ayant pas nécessairement une base dénombrable.