相关论文: Uncertainty principles for orthonormal sequences

We study the maximum norm behavior of $L^2$-normalized random Fourier cosine series with a prescribed large wave number. Precise bounds of this type are an important technical tool in estimates for spinodal decomposition, the celebrated…

We prove the time decay estimates $L^1({\cal R}) \rightarrow L^\infty ({\cal R}),$ where ${\cal R}$ is an infinite star-shaped network, for the Schr\"odinger group $e^{it(- \frac{d^2}{dx^2} + V)}$ for real-valued potentials $V$ satisfying…

In this paper, a temporal nonuniform $L1$ type difference scheme is built up for the time fractional diffusion-wave equation with the help of the order reduction technique. The unconditional convergence of the nonuniform difference scheme…

In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…

In this paper, we study a few versions of the uncertainty principle for the windowed Opdam--Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle,…

In this paper we prove the orthonormal Strichartz estimates for the higher order and fractional Schr\"odinger, wave, Klein-Gordon and Dirac equations with potentials. As in the case of the Schr\"odinger operator, the proofs are based on the…

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…

The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that admits well-defined projections onto the…

This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent…

The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…

Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of…

Using nonstandard methods, we show that the time dependent Fourier series of any smooth function F, solving the wave equation, on a finite closed interval, with vanishing boundary conditions, converges uniformly to F.

We establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small electromagnetic potentials characterized by a dimensionless parameter $\varepsilon\in (0, 1]$ representing the…

We establish a family of uncertainty principles for finite linear combinations of Hermite functions. More precisely, we give a geometric criterion on a subset $S\subset \RR^d$ ensuring that the $L^2$-seminorm associated to $S$ is equivalent…

The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty…

Define a natural number $n$ as a \textit{square-full} integer if for every prime $p$ such that $p|n$, we have $p^2|n$. In this paper, we establish an upper bound on the variance of square-full integers in short intervals of an expected…

We show that whenever $s>k(k+1)$, then for any complex sequence $(\mathfrak a_n)_{n\in \mathbb Z}$, one has $$\int_{[0,1)^k}\left| \sum_{|n|\le N}\mathfrak a_ne(\alpha_1n+\ldots +\alpha_kn^k) \right|^{2s}\,{\rm d}{\mathbf \alpha}\ll…

We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to…