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An example for the holomorphic sectional curvature of the Bergman metric

Żywomir Dinew (2010)

Annales Polonici Mathematici

We study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of its boundary points and moreover the upper limit of the curvature at that point is maximal possible, equal to 2, whereas the lower limit is -∞.

Asymptotic behavior of the sectional curvature of the Bergman metric for annuli

Włodzimierz Zwonek (2010)

Annales Polonici Mathematici

We extend and simplify results of [Din 2010] where the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric in annuli is studied. Similarly to [Din 2010] the description enables us to construct an infinitely connected planar domain (in our paper it is a Zalcman type domain) for which the supremum of the holomorphic sectional curvature is two, whereas its infimum is equal to -∞ .

Bergman coordinates

Steven R. Bell (2006)

Studia Mathematica

Various incarnations of Stefan Bergman's notion of representative coordinates will be given that are useful in a variety of contexts. Bergman wanted his coordinates to map to canonical regions, but they fail to do this for multiply connected regions. We show, however, that it is possible to define generalized Bergman coordinates that map multiply connected domains to quadrature domains which satisfy a long list of desirable properties, making them excellent candidates to be called Bergman representative...

Carleson measure and monogenic functions

S. Bernstein, P. Cerejeiras (2007)

Studia Mathematica

We present necessary and sufficient conditions for a measure to be a p-Carleson measure, based on the Poisson and Poisson-Szegő kernels of the n-dimensional unit ball.

Complétude des noyaux reproduisants dans les espaces modèles

Emmanuel Fricain (2002)

Annales de l’institut Fourier

Soit ( λ n ) n 1 une suite de Blaschke du disque unité 𝔻 et Θ une fonction intérieure. On suppose que la suite de noyaux reproduisants k Θ ( z , λ n ) : = 1 - Θ ( λ n ) ¯ Θ ( z ) 1 - λ n ¯ z n 1 est complète dans l’espace modèle K Θ p : = H p Θ H 0 p ¯ , 1 < p < + . On étudie, dans un premier temps, la stabilité de cette propriété de complétude, à la fois sous l’effet de perturbations des fréquences ( λ n ) n 1 mais également sous l’effet de perturbations de la fonction Θ . On retrouve ainsi un certain nombre de résultats classiques sur les systèmes d’exponentielles. Puis, si on suppose de plus que la suite ...

Continuous Measures on Homogenous Spaces

Michael Björklund, Alexander Fish (2009)

Annales de l’institut Fourier

In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.

Estimates in the Hardy-Sobolev space of the annulus and stability result

Imed Feki (2013)

Czechoslovak Mathematical Journal

The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space H k , ; k * of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L. Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. Math. 46 (1993), 255–269 and by S. Chaabane and I. Feki, Optimal logarithmic estimates in Hardy-Sobolev spaces...

Lp extremal polynomials. Results and perspectives

Laskri, Yamina, Benzine, Rachid (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.Let α = β+γ be a positive finite measure defined on the Borel sets of C, with compact support, where β is a measure concentrated on a closed Jordan curve or on an arc (a circle or a segment) and γ is a discrete measure concentrated on an infinite number of points. In this survey paper, we present a synthesis on the asymptotic behaviour of orthogonal polynomials or Lp extremal polynomials associated to the measure α. We analyze...

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