Thorin classes T (R+),κ > 0, of infinitely divisible distributions on R+ are defined and characterized. Poisson, Karlin and Bessel transforms of Thorin classes are investigated. The extended Thorin classes T (κ)(Rd), κ > 0, are also considered. Canonical representation and selfdecomposability properties of the Thorin subordinated Gaussian Lévy processes are discussed. As an example, the subordi...

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Just over two years ago I wrote a summary of infinite loop space theory [37]. At the time, there seemed to be a lull in activity, with little immediately promising work in progress. As it turns out, there has been so much done in the interim that an update of the summary may be useful. The initial survey was divided into four chapters, dealing with additive infinite loop space theory, multiplic...

Let G be a finite group. For a based G-space X and a Mackey functor M , a topological Mackey functor X e ⊗M is constructed. When X is a based G-CW complex, X e ⊗M is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf’s construction, we get a model for the Eilenberg-Mac Lane spectrum...

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates.