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Let be a -manifold with a Riemannian conformal structure . Given a regular curve on , the authors define a linear operator on the space of (differentiable) vector fields along , only depending on , called the Fermi-Walker connection along . Then, the authors introduce the concept of Fermi-Walker parallel vector field along , proving that such vector fields set up a linear space isomorphic to the tangent space at a point of . This allows to consider the Fermi-Walker horizontal lift of...
We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.
We study the Cauchy problem in the hyperbolic space for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space new phenomena arise, which depend on the properties of the diffusion process in . We also investigate a family of travelling wave solutions, named...
En adaptant les méthodes algébriques et géométriques qu’utilisent M. Sato, T. Kawai et M. Kashiwara pour obtenir le faisceau des microfonctions, nous construisons de manière fonctorielle, donc intrinsèque, un faisceau sur la sphère cotangente à un espace vectoriel réel de dimension finie . Les sections de ce faisceau jouent vis-à-vis des fonctions analytiques sur un rôle analogue à celui des microfonctions vis-à-vis des hyperfonctions. Nous en déduisons une notions de front d’onde à l’infini...
It is shown that Fueter regular functions appear in connection with the Eells condition for harmonicity. New conditions for mappings from 4-dimensional conformally flat manifolds to be harmonic are obtained.
Nikolskii spaces were defined by way of translations on and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in , we get an equivalent definition if we replace translations by all isometries of . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...
The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.
We describe a general axiomatic way to define functions of class Ck, k ∈ N∪{∞} on topological abelian groups. In the category of Banach spaces, this definition coincides with the usual one. The advantage of this axiomatic approach is that one can dispense with the notion of norms and limit procedures. The disadvantage is that one looses the derivative, which is replaced by a local linearizing factor. As an application we use this approach to define C∞ functions in the setting of graded/super manifolds....
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