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math.CA2023
The Fourier transform on valuations is the Fourier transform
Dmitry Faifman, Thomas Wannerer
Alesker has proved the existence of a remarkable isomorphism of the space of translation-invariant smooth valuations that has the same functorial properties as the classical Fourie…
math.CA2011
A Family of Unitary Operators Satisfying a Poisson-type Summation Formula
Dmitry Faifman
We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operat…
math.CA2011
On Multiplicative Maps of Continuous and Smooth Functions
Shiri Artstein-Avidan, Dmitry Faifman, Vitali Milman
In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove…