Construction d'un espace harmonique de Brelot associé à un espace de Dirichlet de type local vérifiant une hypothèse d'hypoellipticite.
Continuité et uniforme continuité du spectre dans les algèbras de Banach
Continuous pluriharmonic boundary values
Let be a bounded hyperconvex domain in and set , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.
Convergence and uniqueness problems for Dirichlet forms on fractals
è un particolare operatore di minimizzazione per forme di Dirichlet definite su un sottoinsieme finito di un frattale che è, in un certo senso, una sorta di frontiera di . Viene talvolta chiamato mappa di rinormalizzazione ed è stato usato per definire su un analogo del funzionale e un moto Browniano. In questo lavoro si provano alcuni risultati sull'unicità dell'autoforma (rispetto a ), e sulla convergenza dell'iterata di rinormalizzata. Questi risultati sono collegati con l'unicità...
Convergence in Dirichlet law of certain stochastic integrals.
Convergence of martingales on manifolds of negative curvature
Convergenza e dualità per forme di Dirichlet non-simmetriche
Convexity of sublevel sets of plurisubharmonic extremal functions
Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.
Corrections to the article “The multivelocity Peierls potential in the problem of refining the classical fundamental acoustic potential near the source of sound in a homogeneous Maxwellian gas”.
Counterexample to Regularity for the Complex Monge-Ampère Equation.
Cramér's formula for Heisenberg manifolds
Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case.
C-semigroups on Banach spaces and functional inequalities
Das Picard-Prinzip und verwandte Fragen bei Störung von harmonischen Räumen.
Delta-plusharmonic functions.
Die L1-Topologie subharmonischer Metriken: Eine Abschätzung und einige Kompaktheitseigenschaften.
Differentiability of excessive functions of one-dimensional diffusions and the principle of smooth fit
The principle of smooth fit is probably the most used tool to find solutions to optimal stopping problems of one-dimensional diffusions. It is important, e.g., in financial mathematical applications to understand in which kind of models and problems smooth fit can fail. In this paper we connect-in case of one-dimensional diffusions-the validity of smooth fit and the differentiability of excessive functions. The basic tool to derive the results is the representation theory of excessive functions;...
Dirchlet's problem on Green lines and some convergence theorems for Denjoy's domains.
Dirichlet forms for general Wentzell boundary conditions, analytic semigroups, and cosine operator functions.
Dirichlet forms on symmetric spaces
Let be a locally compact group and a compact subgroup such that the algebra of biinvariant integrable functions is commutative. We characterize the -invariant Dirichlet forms on the homogeneous space using harmonic analysis of . This extends results from Ch. Berg, Séminaire Brelot-Choquet-Deny, Paris, 13e année 1969/70 and J. Deny, Potential theory (C.I.M.E., I ciclo, Stresa), Ed. Cremonese, Rome, 1970. Every non-zero -invariant Dirichlet form on a symmetric space of non compact type...
Dirichlet problem for quasi-linear elliptic equations.