Related papers: Uniqueness sets for Fourier series

We survey the dimension theory of self-affine sets for general mathematical audience. The article is in Finnish.

This paper deals with a generalized Sudoku problem and investigates the unicity of a given solution. We introduce constraint sets, which is a generalization of the rows, columns and blocks of a classical Sudoku puzzle. The unicity property…

In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.

We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function $f(x)$ which is bounded below by an integrable function, then the series is the Fourier series of $f(x)$ if the…

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality…

We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincar\'e series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the…

We give an extension of Poincar\'e's type capacitary inequality for Dirichlet spaces and provide an application to study the uniqueness sets on the unit circle for these spaces.

In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and…

In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear space…

In this paper we present a new method to study Fourier coefficients of holomorphic and non-holomorphic Eisenstein series simultaneously.

In this paper, we investigate the Fourier transform of self-similar measures on R. We provide quantitative decay rates of Fourier transform of some self-similar measures. Our method is based on random walks on lattices and Diophantine…

Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.

The aim of this article is to draw attention towards various natural but unanswered questions related to the lower central series of the unit group of an integral group ring.

Inter alia, we present a Fourier series involving the generalised Stieltjes constants.

In this article we shows some results about algebra with the group of units having special polynomial identity.

We prove uniqueness of Fourier-Jacobi models for general linear groups, unitary groups, symplectic groups and metaplectic groups, over an archimedean local field.

We introduce discrete wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with corresponding wave-front sets of "continuous type".

A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…

Transition from discrete to continuous Fourier series is studied for the functions becoming singular in the transition. Conditions are specified when summing replacement by integration is inadmissible.

These informal notes briefly discuss various aspects of Cantor sets.