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/ Department of Mathematics and Statistics

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Duncan, Richard


Retired professor

Faculty of Arts and Science - Department of Mathematics and Statistics



Research area

Student supervision Expand all Collapse all

Quelques théorèmes ergodiques pour des suites de fonctions Theses and supervised dissertations / 2011-12
Cyr, Jean-François
Birkhoff’s ergodic theorem gives us information about the convergence of sequences of functions. We are then interested in studying the mean and pointwise convergence of these sequences, but in the case the sequence is a strictly increasing sequence of positive integers. With that goal in mind, we will define uniform sequences and study the pointwise convergence for these sequences. We will also explore the possibility that there exists some sequences for which the convergence of the sequence does not occur. We will present a result of Alexandra Bellow that says that such sequences exist. Finally, we will prove a result which establishes an equivalence between the notion of a strongly mixing transformation and the convergence of a sequence that uses “weights” which satisfies certain properties.

L'évaluation d'un produit dérivé : une apporche discrète Theses and supervised dissertations / 2006
Sabbah, Isaac
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Selected publications Expand all Collapse all

Weak convergence of self-adjoint operators and the generalized spectral theorem

Duncan, R. , Weak convergence of self-adjoint operators and the generalized spectral theorem special volume (2001), , part (2012), , Far East J.Math. Sci. (FJMS),