Related papers: On a problem of Kahane in higher dimensions

We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the…

We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…

In this paper we study the exponential uniform strong summability of two-dimensional Vilenkin-Fourier series. In particular, it is proved that the two-dimensional Vilenkin-Fourier series of the continuous function $f$ is uniformly strong…

At the light of recent results in literature we review a conjecture formulated in Math. Phys. Electron. J. 1 (1995), paper 5, 1--13, about the mechanism of breakdown of invariant sets in KAM problems and the identification of the dominant…

We study the problem of tiling and packing in vector spaces over finite fields, its connections with zeroes of classical exponential sums, and with the Jacobian conjecture

This paper shows that quantization of $\pi$-finite spaces, as a functor out of a higher category of spans, is equivariant in two ways: Symmetries of a given polarization/Lagrangian always induce coherent symmetries of the quantization. On…

We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our…

Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…

We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…

We introduce the "sharp" (universal) extension of a 1-motive (with additive factors and torsion) over a field of characteristic zero. We define the "sharp de Rham realization" by passing to the Lie-algebra. Over the complex numbers we then…

We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as well as in some other situations. This work relies in an…

We document some versions, in real K-theory, of well-known properties of the coarse assembly map in complex K-theory. These results are well-known, but difficult to find in the literature.

In this paper, exact rate of approximation of functions by linear means of Fourier series and Fourier integrals and corresponding $K$-functionals are expressed via special moduli of smoothness. . Introduction is given in $\S 1$. In $\S2$…

We investigate several infinite product of cosines and find the closed form using the Fourier transform. The answers provide limiting distributions for some elementary probability experiments.

We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…

We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which…

A glimpse at $\sum{{\sin(kx)}\over{k}}$ gives a few lines exposition of Fourier series's quadratic mean convergence for square integrable functions and Dirichlet's convergence theorem of the Fourier serie of a piecewise differentiable…

In the present paper, we prove the existence of universal polynomials which express multi-singularity loci classes of prescribed types for proper morphisms between smooth schemes over an algebraically closed field of characteristic zero --…

Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and…

We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint…