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We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for 1 ≤ p ≤ ∞. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.
In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces
x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I.
Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented...
Soient et deux espaces de Krein de fonctions analytiques dans le disque unité invariants pour l’opérateur de déplacement à gauche et soit un opérateur linéaire continu de dans dont l’adjoint commute avec . Nous étudions les dilatations de qui conservent cette propriété de commutation et pour lesquelles les formes hermitiennes définies par et ont le même nombre de carrés négatifs. Nous obtenons ainsi une version du théorème de dilatation des commutants d’opérateurs dans le cadre...
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