Chain sequences and compact perturbations of orthogonal polynomials.
Conditions under which the solutions of a partial difference equations system can be probability functions are examined.When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.
There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.
Given a finite subset of , we study the continuous complex valued functions and the Schwartz complex valued distributions defined on with the property that the forward differences are (in distributional sense) continuous exponential polynomials for some natural numbers .
We give a characterization of the globally Lipschitzian composition operators acting in the space
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.