Girsanov and Feynman–Kac type transformations for symmetric Markov processes
Green functions for killed random walks in the Weyl chamber of Sp(4)
We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 3, there is in this family a walk associated with a reflection group of order 2n. Moreover, the case n = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths...
Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs
Growth of entire -subharmonic functions.
-spaces of conjugate systems on local fields
Hardy-type spaces of harmonic functions on symmetric spaces on noncompact type.
Harmonic functions and Hardy spaces on trees with boundaries
Harmonic Functions of Polynomial Growth on Certain Complete Manifolds.
Harmonic functions on annuli of graphs
Harmonic functions on homogeneous spaces of commutator induced extensions of compact groups
Harmonic functions on multiplicative graphs and interpolation polynomials.
Harmonic Functions on Riemannian Manifolds
Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces
We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball . We then study the Hardy spaces , 0
Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces H... and N*.
Harmonic majorization of in subsets of , .
Harmonic measures for symmetric stable processes
Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and that determine whether ω(S,D) is zero or positive.
Harmonic morphisms and non-linear potential theory
Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic functions h' by hyperharmonic functions u' in this definition, in order to obtain an interesting class of mappings, see [3], Remark 2.3. The modified definition appears to be equivalent with the original one, provided X' is a Bauer space, i.e., a harmonic...
Harmonic morphisms and subharmonic functions.
Harmonic spaces associated with adjoints of linear elliptic operators
Let be an elliptic linear operator in a domain in . We imposse only weak regularity conditions on the coefficients. Then the adjoint exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type given distribution. We then apply to R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of are also studied. The results generalize earlier work of the author.
Harmonic Spaces Associated with Non-Symmetric Translation Invariant Dirichlet Forms.