Lisette Jager

On bounded pseudodifferential operators in a high-dimensional setting

This work is concerned with extending the results of Calderon and Vaillancourt proving the boundedness of Weyl pseudodifferential operators Op W eyl h (F) in L 2 (R n). We state conditions under which the norm of such operators has an upper bound independent of n. To this aim, we apply a decomposition of the identity to the symbol F , thus obtaining a sum of operators of a hybrid type, each of them behaving as a Weyl operator with respect to some of the variables and as an anti-Wick operator with respect to the other ones. Then we establish upper bounds for these auxiliary operators, using suitably adapted classical methods like coherent states.

Exponential Decay of Correlations for a Real-Valued Dynamical System Generated by a k

As a first step towards modelling real time-series, we study a class of real-variable, bounded processes {Xn,n∈N}

k

\{X_{n}, n\in \mathbb{N}\}

Dimensional System

defined by a deterministic k

Bounded Weyl pseudodifferential operators in Fock space

k

On bounded pseudodifferential operators in Wiener spaces

-term recurrence relation Xn+k=φ(Xn,…,Xn+k−1)

Stochastic extensions of symbols in Wiener spaces and heat operator

X_{n+k} = \varphi (X _{n}, \ldots , X_{n+k-1})

Infinite dimensional semiclassical analysis and applications to a model in NMR

. These processes are noise-free. We immerse such a dynamical system into Rk

Lower bounds for pseudodifferential operators with a radial symbol

\mathbb{R}^{k}

Exponential decay of correlations for a real-valued dynamical system embedded in R2

in a slightly distorted way, which allows us to apply the multidimensional techniques introduced by Saussol (Isr. J. Math. 116:223–248, 2000) for deterministic transformations. The hypotheses we need are, most of them, purely analytic and consist in estimates satisfied by the function φ