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Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues

Jean-Pierre Roth (1976)

Annales de l'institut Fourier

Soit X un espace localement compact. Tout opérateur dissipatif de domaine dense dans C 0 ( ( X ) est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où X est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur C 0 ( X ) se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur C 0 ( X ) .À tout opérateur A vérifiant le principe du maximum positif sur C 0 ( X , R ) et de domaine assez riche, on associe un opérateur bilinéaire B , appelé...

Semi-groupes d'opérateurs invariants et opérateurs dissipatifs invariants

Jacques Faraut, Khelifa Harzallah (1972)

Annales de l'institut Fourier

Soit X un espace riemannien symétrique et C 0 ( X ) l’espace des fonctions continues sur X tendant vers 0 à l’infini. On démontre qu’un opérateur ( D A ' , A ) , invariant par les isométries de X , engendre un semi-groupe fortement continu de contractions sur C 0 ( X ) s’il est dissipatif et si son domaine contient les fonctions de classe 𝒞 à support compact.

Square roots of perturbed subelliptic operators on Lie groups

Lashi Bandara, A. F. M. ter Elst, Alan McIntosh (2013)

Studia Mathematica

We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small...

The solution of the Kato problem in two dimensions.

Steve Hofmann, Alan McIntosh (2002)

Publicacions Matemàtiques

We solve, in two dimensions, the "square root problem of Kato". That is, for L ≡ -div (A(x)∇), where A(x) is a 2 x 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2: L12(R2) → L2(R2).[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

Kirchev, Kiril, Borisova, Galina (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.In this paper classes of K^r -operators are considered – the classes of bounded and unbounded operators A with equal domains of A and A*, finite dimensional imaginary parts and presented as a coupling of a dissipative operator and an antidissipative one with real absolutely continuous spectra and the class of unbounded dissipative K^r -operators A with different domains of A and A* and with real absolutely continuous spectra....

Wentzell Boundary Conditions in the Nonsymmetric Case

A. Favini, G. R. Goldstein, J. A. Goldstein, S. Romanelli (2008)

Mathematical Modelling of Natural Phenomena

Let L be a nonsymmetric second order uniformly elliptic operator with generalWentzell boundary conditions. We show that a suitable version of L generates a quasicontractive semigroup on an Lp space that incorporates both the underlying domain and its boundary. This extends the earlier work of the authors on the symmetric case.

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