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harmonic space
Decomposition of a harmonic space and some applications
      
The harmonic space associated with a "reasonable" standard process
      
We also find an analogue of Hesselink formula (see [He]) giving the multiplicity of every simple finite dimensional module in the graded component of the harmonic space in the symmetric algebra.
      
In particular, if the spaceE equipped with the measures satisfies the conditions of a harmonic space, such a Markov process and associated multiplicative functional exist.
      
There is an infinite sequence of conditions {Hk} that the curvature tensor of a harmonic space must satisfy.
      
On a Harmonic Space Satisfying the axioms 1, 2, 3 of M.
      
A solution is given of the generalized Dirichlet problem for an arbitrary compactification of a Brelot harmonic space.
      
Let w=u-v with u, v superharmonic on a suitable harmonic space Ω (for example an open subset of Rn), and let μ[w]=μ[u]-μ[v] denote the associated Riesz charge.
      
In a harmonic space with the domination Axiom (axiom D), B.
      
Let H denote the sheaf of L-solutions, we prove that (Ω,H) is a nonlinear Bauer harmonic space.
      
Integral Representation of Harmonic Functions Defined Outside a Compact Set in a Harmonic Space
      
Given here is an integral representation for any harmonic function u≥0 defined outside a compact set in a Brelot harmonic space Ω with or without positive potentials by means of signed measurers on Ω.
      
Let ? be the family of sheaves H of continuous functions on a Brelot harmonic space Ω with a countable base such that locally the Dirichlet problem with respect to H is solvable, H satisfies Harnack inequalities and also H has a symmetry property.
      
This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric Damek-Ricci space.
      
Then the harmonic space H2 A of the deformation elliptic complex associated with A vanishes.
      
 

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