相关论文: Non-Archimedean pseudodifferential operators and F…
We study the link between pseudo-differential operators and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short-time Fourier transform of the Weyl symbol. This gives…
Let $G$ be a unimodular type I second countable locally compact group and $\hat G$ its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on $G\times\hat G$, and its relations to…
We obtain new semiclassical estimates for pseudodifferential operators with low regular symbols. Such symbols appear naturally in a Cauchy Problem related to recent weak solutions to the unstable Muskat problem constructed via convex…
We establish sharp $L^2$-Sobolev estimates for classes of pseudodifferential operators with singular symbols whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered…
We generalize the results for Banach algebras of pseudodifferential operators obtained by Gr\"ochenig and Rzeszotnik in [24] to quasi-algebras of Fourier integral operators. Namely, we introduce quasi-Banach algebras of symbol classes for…
In this paper we prove local solvability of quasilinear pseudodifferential operators which has homogeneous principal symbol of real principal type. This generalizes Theorem A.1 in arXiv:2403.19054, which treats the case of quasilinear…
We develop a theory of pseudodifferential operators of infinite order for the global classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for…
For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…
We consider a class of equations with the fractional differentiation operator $D^\alpha$, $\alpha >0$, for complex-valued functions $x\mapsto f(|x|_K)$ on a non-Archimedean local field $K$ depending only on the absolute value $|\cdot |_K$.…
The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.
We discuss the recent developments of semi-classical and micro-local analysis in the context of nilpotent Lie groups and for sub-elliptic operators. In particular, we give an overview of pseudo-differential calculi recently defined on…
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory…
In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces…
We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{m}_{0,0}(\mathbb{R}^n)$. We consider wider classes of symbols and improve…
We study some classes of algebras of operators on non-Archimedean Banach spaces. In particular, we propose a non-Archimedean version of the crossed product construction.
In this short note, we consider bilinear pseudo-differential operators with symbols belonging to the Sj\"ostrand class. We show that those operators are bounded from the product of the $L^2$-based Sobolev spaces $H^{s_1} \times H^{s_2}$ to…
We consider the non-homogeneous abstract linear Schr\"odinger and wave equations with zero initial conditions, defined by operators of strip-type and parabola-type in Banach spaces, respectively, and establish the well-posedness of…
Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…
We develop a geometric framework for Weyl quantization on pseudo-Riemannian manifolds, in which pseudodifferential operators act on sections of vector bundles equipped with arbitrary connections. We construct the associated star product and…