This paper investigates the existence of the anisotropic lower-dimensional Minkowski content. We establish that the $C$-anisotropic $k$-dimensional Minkowski content of a $k$-rectifiable compact...

We derive two-sided bounds for a class of Stirling-type asymptotic formulas for piecewise logarithmic interpolations of the pi function, and hence also for the factorials and the gamma functions....

In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.

We present and prove the version of Marstrand's theorem for discrete metric space. We provide explicit estimates of the quotient of upper and lower densities of measures on this space.

We derive an explicit formula for the exponent $β$ in the higher-dimensional fractal uncertainty principle (FUP) established by Cohen 2023, quantifying its dependence on the porosity parameter...

We study the planar Nikodým maximal operator $\mathcal{N}_{Θ;δ}$ associated to a direction set $Θ\subset \mathbb{S}^{1}$. We show that the quasi-Assouad dimension $s :=...

In 1993, Robert Strichartz established a characterization for bounded eigenfunctions of the Laplacian on $\mathbb{R}^d$. Let $\left\{f_k \right\}_{k\in \mathbb{Z}}$ be a doubly infinite sequence...

It is known that Rodrigues formulas provide a very powerful tool to compute orthogonal polynomials with respect to classical weights. We provide an example of bivariate multiple polynomials on the...

We obtain an improved lower bound for the restricted reverse weak-type estimate of the Hardy-Littlewood maximal operator $M$. This result is applied to the $λ$-median maximal operator...

We study the frequency function (introduced by Temur) in both the discrete and continuous settings. More precisely, we extend the definition of the frequency function to the higher-dimensional...

We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by...

This paper deals with Hornich-Hlawka-type and Buzano-type inequalities in inner product spaces (IPS). On the one hand, the Hornich-Hlawka inequality, or Hlawka's inequality, or quadrilateral...

We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by...

The aim of this paper is to provide a complete analysis of the Coulomb equilibrium problem in the euclidean space $\mathbb{R}^d$, $d\geq2$, associated to the kernel $1/|x|^{d-2}$, with a...

The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a Hölder continuous function. The Fourier transform is...