Abstract
Let G be a compactly generated, locally compact group, and let T be the operator of convolution with a probability measure μ on G. Our main results give sufficient conditions on μ for the operator T to be analytic in L p(G), 1 < p < ∞, where analyticity means that one has an estimate of form \(\Vert (I-T)T^n \Vert \leq cn^{-1}\) for all n = 1, 2, ... in L p operator norm. Counterexamples show that analyticity may not hold if some of the conditions are not satisfied.
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Dungey, N. Time Regularity for Random Walks on Locally Compact Groups. Probab. Theory Relat. Fields 137, 429–442 (2007). https://doi.org/10.1007/s00440-006-0006-5
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DOI: https://doi.org/10.1007/s00440-006-0006-5