This paper summarizes some known results about Appell poly nomials and investigates their various analogs. The primary of these are the free Appe ll olynomials. In the multivariate case, they can beâ€¦ (More)

Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients haveâ€¦ (More)

We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only theâ€¦ (More)

The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state, we prove a Favard-type recursion relation. On the otherâ€¦ (More)

A master field is a limiting object in the 1/N expansion of quantum chromodynamics. I give a general introduction to the terminology of quantum field theory. After explaining why the 1/N expansion isâ€¦ (More)

The operatorLÎ¼ : f 7â†’ âˆ« f(x)âˆ’f(y) xâˆ’y dÎ¼(y) is, for a compactly supported measure Î¼ with anL density, a closed, densely defined operator on L(Î¼). We show that the operator Q = pLÎ¼âˆ’qLÎ¼ has polynomialâ€¦ (More)