Related papers: Some spherical uniqueness theorems for multiple tr…

We prove that on separated algebraic surfaces every coherent sheaf is a quotient of a locally free sheaf. This class contains many schemes that are neither normal, reduced, quasiprojective or embeddable into toric varieties. Our methods…

Let $G$ be (the rational points of) a connected reductive group over a local non-archimedean field $F$. In this article we formulate and prove a property of an $F$-spherical homogeneous $G$-space (which in addition satisfies the finite…

Suppose $1 < p < \infty$. Carleson's Theorem states that the Fourier series of any function in $L^p[-\pi, \pi]$ converges almost everywhere. We show that the Schnorr random points are precisely those that satisfy this theorem for every $f…

We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…

This paper deals with properties of filtrations on vector spaces indexed by partially ordered finitely generated abelian groups, which we call multifiltrations. We discuss the usual properties of filtrations, like exhaustivity and…

In the paper we study the multipliers of Fourier series in polynomials orthogonal in continuous-discrete Sobolev's spaces. Multiplier Theorem for Fourier-Sobolev series is obtained. This result is based on the representation of the Fej\'er…

We show that for every finite set of prime numbers S, there are at most finitely many singular moduli that are S-units. The key new ingredient is that for every prime number p, singular moduli are p-adically disperse. We prove analogous…

We give a proof of Fourier extension conjecture on the paraboloid in all dimensions bigger than 2 that begins with a decomposition suggested in Sawyer [Saw8] of writing a smooth Alpert projection as a sum of pieces whose Fourier extensions…

We determine all entire functions $f$ such that for nonzero complex values $a\neq b$ the implications $f=a \Rightarrow f' =a$ and $f' =b \Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…

We prove a Fourier restriction result, uniform over a certain collection of reference measures, for some indices in the Stein-Tomas range.

We present a relation between convergence of multiple and single orthogonal series. This relation implies a complete characterization of all multiple sequences $(a_{n_1...n_d})_{n_1,...,n_d\in\bb N}$ such that for all orthonormal…

Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions. The main result is that the convolution of most arithmetic functions…

We study the $\ell^1$-summability of functions in the $d$-dimensional torus $\mathbb{T}^d$ and so-called $\ell^1$-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the $\ell^1$-norm of their…

We prove the following result. Let f be a continuous function in the closed infinite strip in complex plane. Suppose the restriction of f to every circle inscribed in the strip extends holomorphically inside the circle. Then f is…

Fix integers a_1,...,a_d satisfying a_1 + ... + a_d = 0. Suppose that f : Z_N -> [0,1], where N is prime. We show that if f is ``smooth enough'' then we can bound from below the sum of f(x_1)...f(x_d) over all solutions (x_1,...,x_d) in Z_N…

We prove that in every ring of generalised power series with non-positive real exponents and coefficients in a field of characteristic zero, every series admits a factorisation into finitely many irreducibles of infinite support, the number…

In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. Namely, we prove the a.e. relation $(\frac{1}{n}\sum\limits_{m=0}^{n-1}\left\vert S_{mm}f - f…

We show rigidity results for the operator equations T(f.g) = Tf.Tg, T(f*g) = Tf.Tg and T(f.g) = Tf*Tg for bijective operators T acting on sufficently large spaces of smooth functions. Typically a condition like |T(f.g) - Tf.Tg| < a for all…