Decomposition of polyharmonic functions with respect to the complex Dunkl Laplacian.

Ren, Guangbin; Malonek, Helmuth R.

Displaying similar documents to “Decomposition of polyharmonic functions with respect to the complex Dunkl Laplacian.”

Reproducing kernels for Dunkl polyharmonic polynomials

Kamel Touahri (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree $n$ and Dunkl polyharmonic of degree $m$ , i.e. $Δ_{k}^{m} u = 0$ , $m \in ℕ ∖ {0}$ , where $Δ_{k}$ is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.

"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 Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^{n} \times ℝ^{m}$ , m ≥ 2

Ewa Ligocka (1999)

Annales Polonici Mathematici

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We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.

Monotonicity of Harnack inequality for positive invariant harmonic functions.

Pan, Yifei, Wang, Mei (2007)

Journal of Applied Mathematics and Stochastic Analysis

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Periodic harmonic functions on lattices and points count in positive characteristic

Mikhail Zaidenberg (2009)

Open Mathematics

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This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.