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A calculus for a class of finitely degenerate pseudodifferential operators

Ingo Witt (2003)

Banach Center Publications

For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.

A characterization of elliptic operators

Grzegorz Łysik, Paweł M. Wójcicki (2014)

Annales Polonici Mathematici

We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.

A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators

Paulo D. Cordaro, Nicholas Hanges (2009)

Annales de l’institut Fourier

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let q be a characteristic point for P . We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that P is analytic hypoelliptic at q . Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of...

A Paley-Wiener type theorem for generalized non-quasianalytic classes

Jordi Juan-Huguet (2012)

Studia Mathematica

Let P be a hypoelliptic polynomial. We consider classes of ultradifferentiable functions with respect to the iterates of the partial differential operator P(D) and prove that such classes satisfy a Paley-Wiener type theorem. These classes and the corresponding test spaces are nuclear.

Addition de variables et application à la régularité

Bernard Helffer (1978)

Annales de l'institut Fourier

On montre dans cet article comment des théorèmes récents d’hypoellipticité ou de propagation des singularités peuvent être améliorés par une méthode d’addition de variables qui permet dans certains cas de “désingulariser” l’ensemble caractéristique.

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