Related papers: Analytic hypoellipticity of Keldysh operators

In this paper we study harmonic analysis operators in Dunkl settings associated with finite reflection groups on Euclidean spaces. We consider maximal operators, Littlewood-Paley functions, $\rho$-variation and oscillation operators…

Second order divergence form operators are studied on an open set with various boundary conditions. It is shown that the p-ellipticity condition of Carbonaro-Dragicevic and Dindos-Pipher implies extrapolation to a holomorphic semigroup on…

In $L_2 (\mathbb{R}^d; \mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$ with periodic coefficients depending on $\mathbf{x}/\varepsilon$. We find approximations…

A realization is a triple, $(A,b,c)$, consisting of a $d-$tuple, $A= (A =_1, \cdots, A_d )$, $d\in \mathbb{N}$, of bounded linear operators on a separable, complex Hilbert space, $\mathcal{H}$, and vectors $b,c \in \mathcal{H}$. Any such…

We provide some new sharp assertions on the action of Toeplitz $T_\varphi$ operator in new $F^{p,q}_\alpha$ type spaces of analytic functions of several complex variables extending previously known assertions proved by various authors.

In 1978 M\'etivier showed that a differential operator $P$ with analytic coefficients is elliptic if and only if the theorem of iterates holds for $P$ with respect to any non-analytic Gevrey class. In this paper we extend this theorem to…

Let P and Q be relatively prime integers greater than 1, and f a real valued discretely supported function on a finite dimensional real vector space V. We prove that if f_{P}(x)=f(Px)-f(x) and f_{Q}(x)=f(Qx)-f(x) are both \Lambda-periodic…

Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional…

We consider a one-parameter family of degenerately elliptic operators $\cal{L}_\gamma$ on the closed disk $\mathbb{D}$, of Keldysh (or Kimura) type, which appears in prior work [Mishra et al., Inverse Problems (2022)] by the authors and…

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…

We prove sharp uniform $L^p$-bounds for low-lying eigenfunctions of non-self-adjoint semiclassical pseudodifferential operators $P$ on $\mathbb{R}^{n}$ whose principal symbols are doubly-characteristic at the origin of $\mathbb{R}^{2n}$.…

In this article, we determine the spectrum of real-analytic, non self-adjoint Toeplitz operators on compact K{\"a}hler manifolds and on the complex plane, on neighbourhoods of critical values of the symbol. We consider specifically critical…

For a large class of semiclassical pseudodifferential operators, including Schr\"odinger operators, $ P (h) = -h^2 \Delta_g + V (x) $, on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside…

Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…

For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…

Let $T$ be a bounded linear operator on a Hilbert space $H$ such that \[ \alpha[T^*,T]:=\sum_{n=0}^\infty \alpha_n T^{*n}T^n\ge 0. \] where $\alpha(t)=\sum_{n=0}^\infty \alpha_n t^n$ is a suitable analytic function in the unit disc…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a…

If a differential operator $D$ on a smooth Hermitian vector bundle $S$ over a compact manifold $M$ is symmetric, it is essentially self-adjoint and so admits the use of functional calculus. If $D$ is also elliptic, then the Hilbert space of…

We introduce the concept of $C^{m,\alpha}$-nonlocal operators, extending the notion of second order elliptic operator in divergence form with $C^{m,\alpha}$-coefficients. We then derive the nonlocal analogue of the key existing results for…