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Operator-valued n-harmonic measure in the polydisc

Anders Olofsson (2004)

Studia Mathematica

An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon...

Order functions of plurisubharmonic functions

Halil Celik, Evgeny Poletsky (1997)

Studia Mathematica

We consider the following problem: find on ℂ 2 a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on ℂ ℙ 1 which is constant outside a polar set is the order function of a plurisubharmonic function.

Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data

Alberto Fiorenza, Alain Prignet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We study the sequence u n , which is solution of - div ( a ( x , 𝔻 u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of 𝐑 N and u n = 0 on ∂ Ω , when f n tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N -function Φ , and prove a non-existence result.

Orlicz capacities and applications to some existence questions for elliptic pdes having measure data

Alberto Fiorenza, Alain Prignet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the sequence un, which is solution of - div ( a ( x , ∇ u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N-function Φ, and prove a non-existence result.

Periodic harmonic functions on lattices and points count in positive characteristic

Mikhail Zaidenberg (2009)

Open Mathematics

This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.

Plateau-Stein manifolds

Misha Gromov (2014)

Open Mathematics

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

Plurifine potential theory

Jan Wiegerinck (2012)

Annales Polonici Mathematici

We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.

Pluriharmonic extension in proper image domains

Rafał Czyż (2009)

Annales Polonici Mathematici

Let D j be a bounded hyperconvex domain in ℂ n j and set D = D ₁ × ⋯ × D s , j=1,...,s, s ≥ 3. Also let Ω π be the image of D under the proper holomorphic map π. We characterize those continuous functions f : ∂ Ω π → ℝ that can be extended to a real-valued pluriharmonic function in Ω π .

Currently displaying 361 – 380 of 622