A uniqueness theorem for Riesz potentials

A global Riesz decomposition theorem on trees without positive potentials

We study the potential theory of trees with nearest-neighbor transition probability that yields a recurrent random walk and show that, although such trees have no positive potentials, many of the standard results of potential theory can be transferred to this setting. We accomplish this by defining a non-negative function H, harmonic outside the root e and vanishing only at e, and a substitute ...

A Riesz decomposition theorem on harmonic spaces without positive potentials

In this paper, we give a new definition of the flux of a superharmonic function defined outside a compact set in a Brelot space without positive potentials. We also give a new notion of potential in a BS space (that is, a harmonic space without positive potentials containing the constants) which leads to a Riesz decomposition theorem for the class of superharmonic functions that have a harmonic...

Riesz Transform and Riesz Potentials for Dunkl Transform

Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.

A Uniqueness Theorem for Clustering

Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like “What distinguishes a clustering of data from other data partitioning?”, “Are there any principles governing all clustering paradigms?”, “How should a user choose an appropriate clustering algorithm for a particular task?”, etc. are almost completely unanswered by the e...

The Riesz representation theorem