Related papers: Uncertainty Principles for Fourier Multipliers

A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond…

In this paper, we uncover a new uncertainty principle that governs the complexity of Boolean functions. This principle manifests as a fundamental trade-off between two central measures of complexity: a combinatorial complexity of its…

We prove that in dimension $n\ge 2$ the main singularities of a complex potential $q$ having a certain a priori regularity are contained in the Born approximation $q_{B}$ constructed from backscattering data. This is archived using a new…

This work investigates the Sobolev regularity of solutions to perturbed fractional 1-Laplace equations. Under the assumption that weak solutions are locally bounded, we establish that the regularity properties are analogous to those…

We consider Lurye (sometimes written Lur'e) systems whose nonlinear operator is characterised by a possibly multivalued nonlinearity that is bounded above and below by monotone functions. Stability can be established using a sub-class of…

It is well known that the Fourier--Bohr coefficients of regular model sets exist and are uniformly converging, volume-averaged exponential sums. Several proofs for this statement are known, all of which use fairly abstract machinery. For…

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's…

Inspired by the work of A. Bonami and S. Poornima that a non-constant function which is homogeneous of degree $0$ cannot be a Fourier multiplier on homogeneous Sobolev spaces, we establish analogous results for Fourier multipliers on the…

Let $f$ be a finite signal. The classical uncertainty principle tells us that the product of the support of $f$ and the support of $\hat{f}$, the Fourier transform of $f$, must satisfy $|supp(f)|\cdot|supp(\hat{f})|\geq |G|$. Recently,…

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…

Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by…

New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\bar{\partial} f = \mu \partial f + \nu \overline{\partial f}$ for discontinuous Beltrami coefficients $\mu$ and $\nu$ are obtained,…

In this paper, we develop a quantitative inverse theory for the Gowers uniformity norm $\|\cdot\|_{\mathsf{U}^4}$ in general finite abelian groups. We identify a new type of obstructions to uniformity, which we call almost-cubic…

Chebotar\"ev proved that every minor of a discrete Fourier matrix of prime order is nonzero. We prove a generalization of this result that includes analogues for discrete cosine and discrete sine matrices as special cases. We establish…

We consider an elliptic Kolmogorov equation $\lambda u - Ku = f$ in a separable Hilbert space $H$. The Kolmogorov operator $K$ is associated to an infinite dimensional convex gradient system: $dX = (AX - DU(X))dt + dW (t)$, where $A $ is a…

Using Fourier series representations of functions on axisymmetric domains, we find weighted Sobolev norms of the Fourier coefficients of a function that yield norms equivalent to the standard Sobolev norms of the function. This…

Gowers introduced, for d\geq 1, the notion of dimension-d uniformity U^d(f) of a function f: G -> \C, where G is a finite abelian group and \C are the complex numbers. Roughly speaking, if U^d(f) is small, then f has certain…

We consider a general inhomogeneous parabolic initial-boundary value problem for a $2b$-parabolic differential equation given in a finite multidimensional cylinder. We investigate the solvability of this problem in some generalized…

The purpose of this paper is to develop a Fourier uncertainty principle on compact Riemannian manifolds and contrast the underlying ideas with those arising in the setting of locally compact abelian groups. The key obstacle is the growth of…

For a family of weight functions $h_\kappa$ that are invariant under a reflection group, the uncertainty principle on the unit sphere in the form of $$ \min_{1 \le i \le d} \int_{\mathbb{S}^{d-1}} (1- x_i) |f(x)|^2 h_\kappa^2(x) d\sigma…