If f # L 1 (d+) is harmonic in the space GรK, where + is a radial measure with +(GรK)=1, we have, by the mean value property f = f V +. Conversely, does this mean value property imply that f is harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. R
Some Properties of Boundaries of Symmetric Spaces of Rank One
โ Scribed by Adrian D. Banner
- Book ID
- 110319997
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 183 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0046-5755
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๐ SIMILAR VOLUMES
Let X = G/K be a rank-one Riemannian symmetric space of the noncompact type and letbe the Laplace-Beltrami operator on X. We show that the resolvent operator R(z) of can be meromorphically continued across the spectrum and explicitly determine the poles, i.e. the resonances. Further we describe the
Let X=GรK be a noncompact symmetric space of real rank one. The purpose of this paper is to investigate L p boundedness properties of a certain class of radial Fourier integral operators on the space X. We will prove that if u { is the solution at some fixed time { of the natural wave equation on X
In this paper we investigate L 2 boundedness properties of the Poisson transform associated to a symmetric space of real rank one and prove a related Planchereltype theorem.