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Nous étudions, dans les espaces de Banach, les familles résolvantes (ou pseudo-résolvantes) et les “générateurs” qu’on peut leur associer quand tend vers zéro ou quand tend vers l’infini. Lorsque la famille résolvante est à contraction, ces “générateurs” qu’on peut leur associer quand tend vers zéro ou quand tend vers l’infini. Lorsque la famille résolvante est à contraction, ces “générateurs” vérifient des “principes du maximum” qui sont des versions “abstraites” de principes du maximum...
If denotes the Bessel capacity of subsets of Euclidean -space, , , naturally associated with the space of Bessel potentials of -functions, then our principal result is the estimate: for , there is a constant such that for any set
The study of the equation (L₂L₁)*h = 0 or of the equivalent system L*₂h₂ = -h₁, L*₁h₁ = 0, where is a second order elliptic differential operator, leads us to the following general framework: Starting from a biharmonic space, for example the space of solutions (u₁,u₂) of the system L₁u₁ = -u₂, L₂u₂ = 0, being elliptic or parabolic, and by means of its Green pairs, we construct the associated adjoint biharmonic space which is in duality with the initial one.
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