Related papers: Noncommutative differential transforms for averagi…

Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…

In this paper, we first characterize the polar decomposition of unbounded weighted composition operator pairs $\textbf{C}_{\phi,\omega}$ in an $L^2$-space. Based on this characterization, we introduce the $\lambda$-spherical mean transform…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that…

In this paper we prove the existence of conditional expectations in the noncommutative $L_p(M,\Phi)$ spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we…

We prove variation and oscillation $L^p$-inequalities associated with fractional derivatives of certain semigroups of operators and with the family of truncations of Riesz transforms in the inverse Gaussian setting. We also study these…

We prove the boundedness on $L^p$, $1<p<\infty$, of operators on manifolds which arise by taking conditional expectation of transformations of stochastic integrals. These operators include various classical operators such as second order…

Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…

In this article we characterize all possible cases that may occur in the relations between the sets of $p$ for which weak type $(p,p)$ and strong type $(p,p)$ inequalities for the Hardy--Littlewood maximal operators, both centered and…

We characterize positivity preserving, translation invariant, linear operators in $L^p(\mathbb{R}^n)^m$, $p \in [1,\infty)$, $m,n \in \mathbb{N}$.

In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of operators of order $1$. Namely, assuming that such an…

This paper reviews and advocates against the use of permute-and-predict (PaP) methods for interpreting black box functions. Methods such as the variable importance measures proposed for random forests, partial dependence plots, and…

In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…

We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function $f$ on ${\Bbb R}^2$, for which the map $(A,B)\mapsto f(A,B)$ is Lipschitz in…

The aim of the article is to prove $L^{p}-L^{q}$ off-diagonal estimates and $L^{p}-L^{q}$ boundedness for operators in the functional calculus of certain perturbed first order differential operators of Dirac type for with $p\le q$ in a…

We obtain sharp inequalities for the k-plane transform, the "j-plane to k-plane" transform, and the corresponding dual transforms, acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Some…

For symbol $a\in S^{n(\rho-1)/2}_{\rho,1}$ the pseudo-differential operator $T_a$ may not be $L^2$ bounded. However, under some mild extra assumptions on $a$, we show that $T_a$ is bounded from $L^{\infty}$ to $BMO$ and on $L^p$ for $2\leq…

Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…

This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…

We determine necessary and sufficient conditions on the ring of differential operators of a finite purely inseparable field extension of positive characteristic for determining whether the extension is modular.

Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either…