Related papers: Non-archimedean generalized Bessel potentials and …

In this article, we study a class of non-archimedean pseudo-differential operators associated via Fourier transform to the Bessel potentials. These operators (which we will denote as $J^{\alpha },$ $\alpha >n$) are of the form (J^{\alpha…

We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators…

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the…

In this article we study a class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions. We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we…

Let $S$ be a semi direct product $S=N\rtimes A$ where $N$ is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and $A$ is isomorphic with $\R^k,$ $k>1.$ We consider a class of second order left-invariant…

On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…

In this article we prove that the heat kernel attached to the non-archimedean elliptic pseudodifferential operators determine a Feller semigroup and a uniformly stochastically continuous C_0 transition function of some strong Markov…

Let $\lambda>0$ and $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator on $\mathbb R_+:=(0,\infty)$. We show that the oscillation operator ${\mathcal O(P^{[\lambda]}_\ast)}$ and variation operator…

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…

Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…

Mixed-norm $\alpha$-modulation spaces were introduced recently by Cleanthous and Georgiadis [Trans.\ Amer.\ Math.\ Soc.\ 373 (2020), no. 5, 3323-3356]. The mixed-norm spaces $M^{s,\alpha}_{\vec{p},q}(\mathbb{R}^n)$, $\alpha\in [0,1]$, form…

We study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce…

For certain classes of negative definite symbols $q(x,\xi)$ and state space dependent Bernstein function $f(x,s)$ we prove that $-p(x,D)$, the pseudo-differential operator with symbol $-p(x,\xi)=-f(x,q(x,\xi))$, extends to the generator of…

Let $\mathbb{H}^{n}$ be the Heisenberg group. For $0 \leq \alpha < Q=2n+2$ and $N \in \mathbb{N}$ we consider exponent functions $p(\cdot) : \mathbb{H}^{n} \to (0, +\infty)$, which satisfies H\"older conditions, such that $\frac{Q}{Q+N} <…

The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of…

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in $\mathbb R^n$ under the influence of a variable magnetic field $B$. It incorporates phase factors defined…

In this article, we study a large class of radial probability density functions defined on the p-adic numbers from which it is possible to obtain certain non-archimedean pseudo-differential operators. These operators are associated with…

We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree <3, we prove…

We consider certain constant-coefficient differential operators on $\mathbb{R}^d$ with positive-definite symbols. Each such operator $\Lambda$ with symbol $P$ defines a semigroup $e^{-t\Lambda}$ , $t>0$ , admitting a convolution kernel…

In this paper, we explore a specific class of bi-parameter pseudo-differential operators characterized by symbols $\sigma(x_1,x_2,\xi_1,\xi_2)$ falling within the product-type H\"ormander {class} $\mathbf{S}^m_{\rho, \delta}$. This…