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A Hilbert Lemniscate Theorem in 2

Thomas Bloom, Norman Levenberg, Yu. Lyubarskii (2008)

Annales de l’institut Fourier

For a regular, compact, polynomially convex circled set K in C 2 , we construct a sequence of pairs { P n , Q n } of homogeneous polynomials in two variables with deg P n = deg Q n ...

Approximation et caractère de quasi-analyticité dans la théorie axiomatique des fonctions harmoniques

A. de La Pradelle (1967)

Annales de l'institut Fourier

Dans le cadre de l’axiomatique de M. Brelot, et en utilisant la théorie des fonctions harmoniques adjointes de Madame R.M. Hervé, on caractérise la propriété de quasi-analycité notée A *  : toute fonction harmonique adjointe dans un domaine est nulle dès qu’elle est nulle au voisinage d’un point. On montre que A * est équivalente à une propriété d’approximation de toute fonction réelle finie continue sur les frontières d’ouverts relativement compacts. Cette approximation est réalisée à l’aide de différences...

Boundary potential theory for stable Lévy processes

Paweł Sztonyk (2003)

Colloquium Mathematicae

We investigate properties of harmonic functions of the symmetric stable Lévy process on d without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for...

Characterizations of p-superharmonic functions on metric spaces

Anders Björn (2005)

Studia Mathematica

We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...

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