Related papers: Fourier transform and rigidity of certain distribu…
We prove that a Kakeya set in a vector space over a finite field of size $q$ always supports a probability measure whose Fourier transform is bounded by $q^{-1}$ for all non-zero frequencies. We show that this bound is sharp in all…
Let $D\in\mathbb{N}$, $q\in[2,\infty)$ and $(\mathbb{R}^D,|\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $\mathrm{WE}^{1,\,q}(\mathbb R^D)$ defined…
It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on the…
In this article we prove the existence of sets $E \subseteq \mathbb{R}$ of zero Fourier dimension such that it is possible to restrict the Fourier transform to $E$ on a certain non-trivial range $[1,\tilde{p})$ with $1<\tilde{p}<2$. This…
The strong dual space of linear continuous functionals on a weighted space G of infinitely differentiable functions defined on the real line is described in terms of their Fourier-Laplace transforms.
We extend the result of K. Karlander [Math. Scand. 80 (1997)] regarding finite dimensionality of spaces of absolutely convergent Fourier transforms.
We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but…
The Fourier dimension is not in general stable under finite unions of sets. Moreover, the stability of the Fourier dimension on particular pairs of sets is independent from the stability of the compact Fourier dimension.
Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E/F, and such that F…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…
We propose a framework for a new type of finite field theories based on a hidden duality between an ultra-violet and an infra-red region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of…
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable…
A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy…
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…
Let $X$ be a singular algebraic variety defined over a field $k$, with quotient field $K(X)$. Let $s \geq 2$ be the highest multiplicity of $X$ and $F_s(X)$ the set of points of multiplicity $s$. If $Y\subset F_s(X)$ is a regular center and…
We introduce a framework to prove integral rigidity results for the Seiberg-Witten invariants of a closed $4$-manifold $X$ containing a non-separating hypersurface $Y$ satisfying suitable (chain-level) Floer theoretic conditions. As a…
A Double Field Theory (DFT) description of gauge symmetry enhancing-breaking in the heterotic string is presented. The construction, based on previous results for the bosonic string, relies on the extension of the tangent frame of DFT. The…
Let $G$ be an even orthogonal quasi-split group defined over a local non-archimedean field $F$. We describe the subspace of smooth vectors of the minimal representation of $G(F),$ realized on the space of square-integrable functions on a…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…