Related papers: Some results related to the Logvinenko-Sereda theo…

In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…

We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.

Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we…

For each $f\!:\!\mathbb{R}\to\mathbb{C}$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrable functions in the Alexiewicz norm, it is shown that the…

We provide necessary and sufficient geometric conditions for the exact observability of the Schr\"odinger equation with inverse-square potentials on the half-line. These conditions are derived from a Logvinenko-Sereda type theorem for…

We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier…

This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…

A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all $L^{p}$ spaces, $1\leq p < \infty$. We obtain new results on…

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and…

This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity…

Using Kakichev's classical concept and extending Yakubovich-Britvina's approach (\textit{Results. Math.} 55(1-2):175-197, 2009) and (\textit{Integral Transforms Spec. Funct.} 21(4):259--276, 2010) for setting up Kontorovich-Lebedev…

An analogue of D. Waterman's result on the summability of the Fourier series for functions of bounded \Lambda-variation by the Ces\'aro methods of negative order is obtained in multidimensional case. It is proved that, unlike…

We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…

We prove that subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some asymptotically small sets on spheres, are bounded from above everywhere. It follows that subharmonic functions of…

The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…

The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…

Eremenko and Lyubich proved that an entire function whose set of singular values is bounded is expanding at points where its image has large modulus. These expansion properties have been at the centre of the subsequent study of this class…

We give $L^1$-norm estimates for exponential sums of a finite sets $A$ consisting of integers or lattice points. Under the assumption that $A$ possesses sufficient multidimensional structure, our estimates are stronger than those of…

In this article we prove a multidimensional version of the Nazarov lemma. The proof is based on an appropriate generalisation of the regularised system of intervals introduced by Havin, Nazarov and Mashreghi to several dimensions.

We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…