Local uniform linear convexity with respect to the Kobayashi distance.
Local vs. global hyperconvexity, tautness or -completeness for unbounded open sets in
Some known localization results for hyperconvexity, tautness or -completeness of bounded domains in are extended to unbounded open sets in .
Logarithmic Growth of the Bergman Kernel for Weakly Pseudoconvex Domains in ...3 of Finite Type.
Lower bounds for norms of products of polynomials on spaces
For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on , whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes . For p > 2 we present some estimates on the constants involved.
Lp continuity of projectors of weighted harmonic Bergman spaces.
Maps from the Two-Ball to the Three-Ball.
Matrices of positive polynomials.
Maximum module principle for power series on a Banach algebra.
Maximum modulus in a bidisc of analytic functions of bounded -index and an analogue of Hayman’s theorem
We generalize some criteria of boundedness of -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).
Maximum modulus sets
We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain of dimension . If is a smooth manifold of dimension and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in with the same smooth -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in vanishes or if is polynomially...
Maximum modulus sets and reflection sets
We study sets in the boundary of a domain in , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to reflection sets, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.
m-Berezin transform and compact operators.
m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary...
Mean growth and Fourier coefficients of some classes of holomorphic functions on bounded symmetric domains
Mean value theorems for harmonic and holomorphic functions on bounded symmetric domains.
Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines
Soit un compact polynomialement convexe de et son “potentiel logarithmique extrémal” dans . Supposons que est régulier (i.e. continue) et soit une fonction holomorphe sur un voisinage de . On construit alors une suite de polynôme de variables complexes avec deg pour , telle que l’erreur d’approximation soit contrôlée de façon assez précise en fonction du “pseudorayon de convergence” de par rapport à et du degré de convergence . Ce résultat est ensuite utilisé pour étendre...
Meilleures estimations possibles pour l'ensemble des points algébriques de fonctions analytiques.
Meromorphe Funktionen auf allgemeinen komplexen Räumen.
Meromorphic extension of holomorphic functions with growth conditions
Meromorphic functions and analytic cycles. (Fonctions méromorphes et cycles analytiques.)
Meromorphic Mappings onto Compact Complex Spaces of General Type.