Transformations of Moment Functionals

Multivariate Orthogonal Polynomials and Modified Moment Functionals

Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree 2, respectively. Orthogonal polynomia...

Local Graph Transformations Driven by Lyapunov Functionals

We study the dynamical behavior of automata networks defined by x(t + 1) = x(t) + f(Ax(t) + b); where A is a symmetric n x n matrix, b is a real n-vector and f is the subgradient of a convex function . More precisely we prove, by using Lyapunov operators associated to the network, that the steady state behavior of these automata is simple: fixed points or two-cycles. We also give bounds for the...

Quasi-definiteness of Generalized Uvarov Transforms of Moment Functionals

When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {Pn(x)}∞n=0, we consider a point masses perturbation τ of σ given by τ := σ+ λ ∑m l=1 ∑ml k=0((−1) ulk/k!)δ (x− cl), where λ, ulk, and cl are constants with ci = cj for i = j. That is, τ is a generalized Uvarov transform of σ satisfying A(x)τ = A(x)σ, where A(x) = ∏m l=1(x− cl) l. We find necessary and suff...

A fourth moment inequality for functionals of stationary processes

In this paper, a fourth moment bound for partial sums of functional of strongly ergodic Markov chain is established. This type of inequality plays an important role in the study of empirical process invariance principle. This one is specially adapted to the technique of Dehling, Durieu and Volný (2008). The same moment bound can be proved for dynamical system whose transfer operator has some sp...

Representation of nonlinear transformations and functionals on LP spaces