Related papers: Projective Pseudodifferential Analysis and Harmoni…

A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…

In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.

A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…

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 $m$…

Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…

In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…

We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…

In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We will show that a global pseudo-differential calculus can be…

As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions $u$ with compact spectra. The estimate is a factorisation inequality, in which one…

This paper has been withdrawn by the authors. A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those…

We present in this paper the construction of a pseudodifferential calculus on smooth non-compact manifolds associated to a globally defined and coordinate independant complete symbol calculus, that generalizes the standard…

A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on…

We produce, on general homogeneous groups, an analogue of the usual H\"ormander pseudodifferential calculus on Euclidean space, at least as far as products and adjoints are concerned. In contrast to earlier works, we do not limit ourselves…

We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked…

Consider an h-pseudodifferential operator P, whose symbol extends holomorphically to a tubular neighborhood of the real phase space and converges sufficiently fast to 1, so that the determinant of P is well-defined. We show that the modulus…

Following previous works for the unit ball, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in…

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…

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 aim at extending the definition of the Weyl calculus to an infinite dimensional setting, by replacing the phase space $ \mathbb{R}^{2n}$ by $B^2$, where $(i,H,B)$ is an abstract Wiener space. A first approach is to generalize the…