Related papers: Spectral Multipliers on 2-step Stratified Groups, …

Let L be a non-negative, self-adjoint operator on L^2(\Omega), where (\Omega, d \mu) is a space of homogeneous type. Assume that the semigroup {T_t}_{t>0} generated by -L satisfies Gaussian bounds, or more generally Davies-Gaffney…

Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.

We discuss in which cases the Dunkl convolution of distributions, possibly both with non-compact support, can be defined and study its analytic properties. We prove results on the (singular-)support of Dunkl convolutions. Based on this, we…

A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…

Let $L$ be a positive self-adjoint operator on $L^2(X)$, where $X$ is a $\sigma$-finite metric measure space. When $\alpha \in (0,1)$, the subordinated semigroup $\{\exp(-tL^{\alpha}):t \in \mathbb{R}^+\}$ can be defined on $L^2(X)$ and…

We consider the problem of learning convolution operators associated to compact Abelian groups. We study a regularization-based approach and provide corresponding learning guarantees under natural regularity conditions on the convolution…

We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits a partition (stratification) into smooth manifolds (strata)…

For the simple Lie algebra $ \frak{so}_m$, we study the commutant vertex operator algebra of $ L_{\hat{\frak{so}}_{m}}(n,0)$ in the $n$-fold tensor product $ L_{\hat{\frak{so}}_{m}}(1,0)^{\otimes n}$. It turns out that this commutant vertex…

We study a class of left-invertible operators which we call weakly concave operators. It includes the class of concave operators and some subclasses of expansive strict $m$-isometries with $m > 2$. We prove a Wold-type decomposition for…

Let $(M,g)$ be a complete non-compact Riemannian manifold. We consider operators of the form $\Delta_g + V$, where $\Delta_g$ is the non-negative Laplacian associated with the metric $g$, and $V$ a locally integrable function. Let $\rho :…

In this article, we get the spectral solution $\mathcal{P}_{\mu}^{m}$ of operators $m(\mathcal{L}, -\Delta_\mathfrak{z})$, the joint functional calculus of the sub-Laplacian and Laplacian on the centre of M\'etivier group. Then, we give…

The aim of this paper is to find new estimates for the norms of functions of the (minus) Laplace operator $\cal L$ on the `$ax+b$' groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type…

The evolution kernels that govern the scale dependence of the generalized parton distributions are invariant under transformations of the $\mathrm{SL}(2,\mathrm R)$ collinear subgroup of the conformal group. Beyond one loop the symmetry…

We characterize the boundedness of a positive integral operator $T_K$, with kernel $K\in M_+(\R^{2n})$, between Lorentz-Gamma spaces $\Gamma_{p,\phi_2}(\R^n)$ and $\Gamma_{q,\phi_1}(\R^n)$, $1<p\le q<\infty$. The key step reduces the…

The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…

In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…

The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl $m$-function. This general result is applied to different self-adjoint realizations of second-order elliptic…

There are important conjectures about logarithmic conformal field theories (LCFT), which are constructed as kernel of screening operators acting on the vertex algebra of the rescaled root lattice of a finite-dimensional semisimple complex…

Let $\mathscr{A}$ be a unital C$^*$-algebra and $E_n$ be the Hilbert $\mathscr{A}$-module defined as the completion of the $\mathscr{A}$-valued Schwartz function space $\mathcal{S}^\mathscr{A}(\mathbb{R}^n)$ with respect to the norm…

With a help of the Schwinger --- DeWitt expansion analytical properties of the evolution operator kernel for the Schr\"odinger equation in time variable $t$ are studied for the Coulomb and Coulomb-like (which behaves themselves as $1/|\vec…