Mixing operators and small subsets of the circle

By Fr'ed'eric Bayart, É. Matheron. 2011

57 citations recorded by the source corpus.

We provide complete characterizations, on Banach spaces with cotype 2, of those linear operators which happen to be weakly mixing or strongly mixing transformations with respect to some nondegenerate Gaussian measure. These characterizations involve two families of small subsets of the circle: the countable sets, and the so-called sets of uniqueness for Fourier-Stieltjes series. The most interesting part, i.e. the sufficient conditions for weak and strong mixing, is valid on an arbitrary (complex, separable) Fr\'echet space.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/79837cd0bf6fd153894987f741450348d45f403c

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In Mathematical Physics

1. Quentin Menet
2. É. Matheron
3. S. Grivaux
4. Antonio Bonilla
5. K. Grosse-Erdmann
6. Fr'ed'eric Bayart

Citations in the corpus

• Linear chaos and frequent hypercyclicity (2014, background): “4] and can be found in many papers [8,11,17,20,24,27].”
• Linear dynamical systems on Hilbert spaces: typical properties and explicit examples (2017, background): “By [9], it follows that T is strongly mixing in the Gaussian sense.”