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Fronts d'onde à l'infini des fonctions analytiques réelles

Jean-Louis Lieutenant (1984)

Annales de l'institut Fourier

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 𝒞 t sur la sphère cotangente à un espace vectoriel réel de dimension finie E . Les sections de ce faisceau jouent vis-à-vis des fonctions analytiques sur E un rôle analogue à celui des microfonctions vis-à-vis des hyperfonctions. Nous en déduisons une notions de front d’onde à l’infini...

Fueter regular mappings and harmonicity

Wiesław Królikowski (1996)

Annales Polonici Mathematici

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.

Function spaces of Nikolskii type on compact manifold

Cristiana Bondioli (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Nikolskii spaces were defined by way of translations on R n and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in R n , we get an equivalent definition if we replace translations by all isometries of R n . 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...

Functional equations in real-analytic functions

G. Belitskii, V. Tkachenko (2000)

Studia Mathematica

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.

Functions of class Ck without derivatives.

Gijs M. Tuynman (1997)

Publicacions Matemàtiques

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....

Functions with prescribed singularities

Giovanni Alberti, S. Baldo, G. Orlandi (2003)

Journal of the European Mathematical Society

The distributional k -dimensional Jacobian of a map u in the Sobolev space W 1 , k − 1 which takes values in the sphere S k − 1 can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M of codimension k can be realized as Jacobian of a Sobolev map valued in S k − 1 . In case M is polyhedral, the map we construct...

Functorial prolongations of Lie groupoids

Ivan Kolář (2007)

Banach Center Publications

For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.

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