360 research outputs found
Every P-convex subset of is already strongly P-convex
A classical result of Malgrange says that for a polynomial P and an open
subset of the differential operator is surjective on
if and only if is P-convex. H\"ormander showed that
is surjective as an operator on if and only if
is strongly P-convex. It is well known that the natural question
whether these two notions coincide has to be answered in the negative in
general. However, Tr\`eves conjectured that in the case of d=2 P-convexity and
strong P-convexity are equivalent. A proof of this conjecture is given in this
note
Thermoacoustic tomography with variable sound speed
We study the mathematical model of thermoacoustic tomography in media with a
variable speed for a fixed time interval, greater than the diameter of the
domain. In case of measurements on the whole boundary, we give an explicit
solution in terms of a Neumann series expansion. We give necessary and
sufficient conditions for uniqueness and stability when the measurements are
taken on a part of the boundary
Entire cyclic homology of continuous trace algebras
A central result here is the computation of the entire cyclic homology of
canonical smooth subalgebras of stable continuous trace C*-algebras having
smooth manifolds M as their spectrum. More precisely, the entire cyclic
homology is shown to be canonically isomorphic to the continuous periodic
cyclic homology for these algebras. By an earlier result of the authors, one
concludes that the entire cyclic homology of the algebra is canonically
isomorphic to the twisted de Rham cohomology of M.Comment: 7 pages, Latex2e, minor typos correcte
Équations aux dérivées partielles inhomogènes à coefficients constants dépendant de paramètres
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