Related papers: Spectral identities and smoothing estimates for ev…

This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and…

Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…

We consider stochastic smoothing of spectral functions of matrices using perturbations commonly studied in random matrix theory. We show that a spectral function remains spectral when smoothed using a unitarily invariant perturbation…

We consider a minimal residual discretization of a simultaneous space-time variational formulation of parabolic evolution equations. Under the usual `LBB' stability condition on pairs of trial- and test spaces we show quasi-optimality of…

We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…

Time series forecasting is an active research topic in academia as well as industry. Although we see an increasing amount of adoptions of machine learning methods in solving some of those forecasting challenges, statistical methods remain…

We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…

In this paper we prove the first result of Nekhoroshev stability for steep Hamiltonians in H\"older class. Our new approach combines the classical theory of normal forms in analytic category with an improved smoothing procedure to…

We obtain an integral formula for the distribution of the first hitting time of the origin for one-dimensional $\alpha$-stable processes $X_t$, where $\alpha\in(1,2)$. We also find a spectral-type integral formula for the transition…

Let $\Delta_{\mathbb{T}^m\times \mathbb{R}^n}$ denote the Laplace-Beltrami operator on the product spaces $\mathbb{T}^m\times \mathbb{R}^n$. In this article we show that $$ \left\|e^{it\Delta_{\mathbb{T}^m\times…

We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…

This work is devoted to the study of uncertainty principles for finite combinations of Hermite functions. We establish some spectral inequalities for control subsets that are thick with respect to some unbounded densities growing almost…

We extend a result of Davies and Nath on the location of eigenvalues of Schr\"odinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context, we also discuss various examples related to the…

A host algebra of a (possibly infinite dimensional) Lie group $G$ is a $C^*$-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations $\pi \colon G \to \U(\cH)$. In this paper we present…

Consider the motion of a viscous incompressible fluid in a 3D exterior domain when a rigid body moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, $L^q$-$L^r$ smoothing…

This work establishes new results on spectral theory and time evolution for matrix-valued discrete Schr\"odinger operators on the space of square-summable matrix sequences. The matrix-valued formalism is employed to streamline notation,…

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…

We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…

The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…

In this paper we show the invariance of the Fredholm index of non-smooth pseudodifferential operators with coefficients in H\"older spaces. By means of this invariance we improve previous spectral invariance results for non-smooth…