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We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…
These are notes of a talk based on the work arXiv:1212.3630 joint with A. Aizenbud. Let V be a finite-dimensional vector space over a local field F of characteristic 0. Let f be a function on V of the form $f(x)= \psi (P(x))$, where P is a…
We provide, among other things: (i) a Bousfield--Kan formula for colimits in $\infty$-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) $\infty$-categorical generalizations…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We show that the function Li_s(e^x) extends to an entire function of the complex variable s, taking values in tempered distributions in x on the whole real line. That the classical polylogarithm extends similarly, as an entire function…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
The procedure of the holonomy-flux algebra construction along a piecewise linear path, which consists of a countably infinite number of pieces, is described in this article. The related construction approximates the continuous distribution…
We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$, as well as a certain duality for the $E_n$-(co)homology of…
An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…
We use Floer theory to describe invariants of symplectic $\mathbb{C}^*$-manifolds admitting several commuting $\mathbb{C}^*$-actions. The $\mathbb{C}^*$-actions induce filtrations by ideals on quantum cohomology, as well as filtrations on…
We study the short-time Fourier transform on the space $\mathcal{K}_{1}'(\mathbb{R}^n)$ of distributions of exponential type. We give characterizations of $\mathcal{K}_{1}'(\mathbb{R}^n)$ and some of its subspaces in terms of modulation…
We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…
The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (1) $\mathcal{C}^\infty$…
We prove a Slice Theorem around closed leaves in a singular Riemannian foliation, and we use it to study the $C^\infty$-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G.~Schwarz. In…
We relate the recognition principle for infinite $\mathbf P^1$-loop spaces to the theory of motivic fundamental classes of D\'eglise, Jin, and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
We study the distribution of families of multiplicative functions among the coprime residue classes to moduli varying uniformly in a wide range, obtaining analogues of the Siegel--Walfisz Theorem for large classes of multiplicative…
We study the class $\mathcal{M}_{\mathrm{ratio}}$ of those probability distributions for which the free $R$-transforms are rational functions. This class is closed under the additive free convolution, additive free powers and under the…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…