Subharmonic functions and their Riesz measure.
Subharmonic functions in sub-Riemannian settings
In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution . These characterizations are based on suitable average operators on the level sets of . Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks. We analyze as well the notion of subharmonic function...
Subharmonic Functions on Real and Complex Manifolds.
Subharmonicity for areal Bloch-function criteria
Subharmonicity in von Neumann algebras
Let ℳ be a von Neumann algebra with unit . Let τ be a faithful, normal, semifinite trace on ℳ. Given x ∈ ℳ, denote by the generalized s-numbers of x, defined by = inf||xe||: e is a projection in ℳ i with ≤ t (t ≥ 0). We prove that, if D is a complex domain and f:D → ℳ is a holomorphic function, then, for each t ≥ 0, is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.
Substochastic transition operators on trees and their associated Poisson integrals
Suites définies négatives et espaces de Dirichlet sur la sphère
Sul problema di Dirichlet in un cono per l’equazione
Sul problema pluriarmonico in un campo sferico di per
Let be the boundary of the unit ball of . A set of second order linear partial differential operators, tangential to , is explicitly given in such a way that, for , the corresponding PDE caractherize the trace of the solution of the pluriharmonic problem (either “in the large” or “local”), relative to .
Sums of Continuous Plurisubharmonic Functions and the Complex Monge-Ampère Operator in ....n.
Superharmonic extension and harmonic approximation
Let be an open set in and be a subset of . We characterize those pairs which permit the extension of superharmonic functions from to , or the approximation of functions on by harmonic functions on .
Superharmonic functions and bounded point evaluations.
Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms.
Superharmonic functions on Lipschitz domain
Superharmonicity of nonlinear ground states.
The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operatorΔpu = div (|∇u|p-2 ∇u)is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δp is the positive solution with boundary values zero of the equationdiv(|∇u|p-2 ∇u) + λ |u|p-2 u = 0in the bounded domain Ω in the n-dimensional Euclidean space.
Superlinear CG convergence for special right-hand sides.
Sur certaines questions qui se rattachent au problème de Dirichlet
Sur la comparaison des deux types d'effilement
Sur la convergence radiale des potentiels associés à l'équation de Helmholtz
Sur la fonction de Green pour un domaine fin
Dans le cadre axiomatique de M. Brelot et R.-M. Hervé (cas y compris l’axiome de domination) on montre que, pour tout domaine par rapport à la topologie fine et pour tout point , la fonction (“fine ”) de Green pour à pôle est caractérisée (à un facteur constant près) comme un potentiel fin relatif à qui est finement harmonique dans .