121026309
A note on extended regular functional spaces
118523806
Condensor principle and the unit contraction
Deny introduced in [4] the notion of functional spaces by generalizing Dirichlet spaces. In this paper, we shall give the following necessary and sufficient conditions for a functional space to be a real Dirichlet space. Let be a regular functional space with respect to a locally compact Hausdorff space X and a positive measure ξ in X . The following four conditions are equivalent.
121054335
Remarque sur la somme d'un noyau de Dirichlet et du noyau newtonien
117210803
Sur les fonctions polyharmoniques et le problème de Riquier
Soit Ω un ouvert de l’espace euclidien R n a n(≧2) dimensions. Les recherches des fonctions harmoniques dans Ω sont essentielles dans la theorie classique du potentiel. A ce moment-la, il est bien connu que le balayage pour le noyau de Green dans Ω joue un grand role (par example, cf. M. Brelot [1]).
121930641
On kernels of invariant functional spaces
Introduction. Deny introduced in [6] the notion of invariant functional spaces and he proved that to an invariant functional space ZE corresponds a convolution kernel ic in the following sense: each potential u f in ZE generated by a bounded measurable function f with compact support is equal to the convolution ic *f. In this paper, we shall prove that the converse is valid. That is, for a positive measure ic of positive type, there exists an invariant functional space with kernel ic. Furthermore we shall give a necessary and sufficient condition for a positive measure ic of positive type to be the kernel of a special Dirichlet space. 1. Invariant functional spaces, Let X be a locally compact abelian group. We denote by dx the Haar measure of X. We define two kinds of functional spaces on X. Definition 1. A weak invariant functional space ZE=E(X) with respect to X and dx is a Hilbert space of real valued locally summable functions satisfying the following two conditions. (1.1) For any compact subset K in X, there exists a positive constant A(K) such that
121611706
Remarks on Ninomiya's domination principle
43214281
A note on the paper "Disjunctive languages and compatible orders"
Dans un article anterieur, nous avons etudie les langages m-disjonctifs et s-disjonctifs sur un alphabet X ainsi que les relations d'ordre partiel compatibles qui leur sont associees. Cependant, nous n'avions considere jusqu'a present que des alphabets d'au moins deux lettres. Dans cette note, nous traitons le cas d'un alphabet a une lettre et nous montrons que tout langage disjonctif sur un alphabet a une lettre est s-disjonctif