Displaying similar documents to “Asymptotic behaviour of harmonic polynomials bounded on a compact set”

Unbounded harmonic functions on homogeneous manifolds of negative curvature

Richard Penney, Roman Urban (2002)

Colloquium Mathematicae

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We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove...

Growth and asymptotic sets of subharmonic functions (II)

Jang-Mei Wu (1998)

Publicacions Matemàtiques

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We study the relation between the growth of a subharmonic function in the half space R and the size of its asymptotic set. In particular, we prove that for any n ≥ 1 and 0 < α ≤ n, there exists a subharmonic function u in the R satisfying the growth condition of order α : u(x) ≤ x for 0 < x < 1, such that the Hausdorff dimension of the asymptotic set ∪A(λ) is exactly n-α. Here A(λ) is the set of boundary points at which...