Cesare Parenti

Propagation of Singularities for Fuchsian Operators

Preliminaries and review of results of N. Hanges.- General fuchsian systems.- Applications to Fuchsian hyperbolic P.D.E..- Operators with multiple non-involutive characteristics.

A Generalization of Hörmander's Inequality-I

We give sufficient conditions to generalize Hörmanders inequality to the case of operators with multiple characteristics of order higher than two

Lower Bounds for Pseudodifferential Operators

We start off by fixing some notation (see Sjostrand [6]). Let X be an open subset of R n (more generally, X can be a C ∞ n-dimensional manifold without boundary) and let ∑ ⊂ T * (X\0 ≃. X × (R n \{0}) be a C∞ conic sub-manifold. With µ∈ R and h ∈ Z + = {0, 1, 2,…}, we denote by N µ,h (X, ∑) the set of all classical symbols of order µ, p(x,ξ) ∼ ∑ j ≥0 p µ-j (x, ξ), such that for any j ≥ 0 one has

On the Cauchy Problem for Hyperbolic Operators with Double Characteristics

\left| {{{p}_{{\mu - j}}}\left( {x,\xi } \right)} \right|{\underset{\raise0.3em\hbox{

Lower Bound Estimates Without Transversal Ellipticity

\smash{\scriptscriptstyle\thicksim}

A Note on Kohn’s and Christ’s Examples

}}{ < }}{{\left| \xi \right|}^{{\mu - j}}}dis{{t}_{\Sigma }}{{\left( {x,\xi } \right)}^{{{{{\left( {h - 2j} \right)}}_{ + }}}}}

A necessary and sufficient condition for a lower bound for fourth-order pseudodifferential operators

where t + =max{t, 0} and dist∑(x,ξ) denotes the distance of x,ξ/∣ξ∣) to{ ( y,η) ∈ ∑;∣η∣ =1}. OPNμ,h (X, ∑) will then denote the corresponding

Diagonalizzabilità e forme normali

We study the C ∞ well-posedness of the Cauchy problem for a class of hyperbolic second order operators with double characteristics in presence of geometric transitions.