Related papers: Two-Spectra Theorem with Uncertainty
Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schr\"odinger operators are extended to allow singular potentials such as certain $L^p$-functions. The proof is based on accordingly adapted Carleman…
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the…
The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…
We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr\"odinger operator determines the potential. Our…
For the one-dimensional Schr\"odinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides…
We provide a simple and short proof of a multidimensional Borg-Levinson type theorem. Precisely, we prove that the spectral boundary data determine uniquely the corresponding potential appearing in the Sch\"odinger operator on an admissible…
Generalized spectra of differential operators can be related to spectra of preconditioned discretized operators. Obtaining (estimates of) the eigenvalues of the preconditioned discretized operators may lead to better estimating of the…
This paper aims to investigate the pseudo-modes of the one-dimensional Schr\"odinger operator with complex potentials, focusing on the behavior of the resolvent norm along specific curves in the complex plane and assessing the stability of…
Dealing with one-dimensional diffusion operators, we obtain upper and lower variational formulae on the eigenvalues given by the max-min principle, generalizing the celebrated result of Chen and Wang on the spectral gap. Our inequalities…
We make a spectral analysis of discrete Schroedinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal spectral enclosures are obtained for summable potentials.…
Multiparameter maximal estimates are considered for operators of Schr\"odinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
We explore spectral duality in the context of measures in $\br^n$, starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogonal bases of complex exponentials in $L^2(\Omega)$ and…
This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…
We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…
A number of results on radial positive definite functions on ${\mathbb R^n}$ related to Schoenberg's integral representation theorem are obtained. They are applied to the study of spectral properties of self-adjoint realizations of two- and…
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among…