68 research outputs found
The Dirichlet Problem for Harmonic Functions on Compact Sets
For any compact set we develop the theory of Jensen
measures and subharmonic peak points, which form the set , to
study the Dirichlet problem on . Initially we consider the space of
functions on which can be uniformly approximated by functions harmonic in a
neighborhood of as possible solutions. As in the classical theory, our
Theorem 8.1 shows for compact sets with
closed. However, in general a continuous solution cannot be
expected even for continuous data on \rO_K as illustrated by Theorem 8.1.
Consequently, we show that the solution can be found in a class of finely
harmonic functions. Moreover by Theorem 8.7, in complete analogy with the
classical situation, this class is isometrically isomorphic to
for all compact sets .Comment: There have been a large number of changes made from the first
version. They mostly consists of shortening the article and supplying
additional reference
Combinatorics and invariant differential operators on multiplicity free spaces
We study the generalization of shifted Jack polynomials to arbitrary
multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that
these polynomials are eigenfunctions for commuting difference operators. Our
central result now is the "transposition formula", a generalization of
Okounkov's binomial theorem (q-alg/9608021) for shifted Jack polynomials. From
this formula, we derive an interpolation formula, an evaluation formula, a
scalar product, a binomial theorem, and properties of the algebra generated by
the multiplication and difference operators.Comment: 36 pages, some typos correcte
Représentation intégrale de certaines séries de fonctions sphériques d'un système de racines BC
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