Unbounded harmonic functions on homogeneous manifolds of negative curvature

• Autorzy: Richard Penney , Roman Urban
• Języki publikacji: EN

Abstrakty

EN

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 some theorems answering partially the following question. Is a given harmonic function the Poisson integral of "something" from the boundary N?

Kategorie tematyczne

• 31B25: Boundary behavior
• 22E25: Nilpotent and solvable Lie groups
• 43A85: Analysis on homogeneous spaces
• 53C30: Homogeneous manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 91
• Numer: 1
• Strony: 99-121

Daty

wydano

2002

Twórcy

autor

Richard Penney

• Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.

autor

Roman Urban

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm91-1-8