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An application of multivariate total positivity to peacocks

Antoine Marie Bogso (2014)

ESAIM: Probability and Statistics

We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of [F. Hirsch, C. Profeta, B. Roynette and M. Yor, Peacocks and associated martingales vol. 3. Bocconi-Springer (2011)], our guiding example is the result of Carr−Ewald−Xiao [P. Carr, C.-O. Ewald and Y. Xiao, Finance Res. Lett. 5 (2008) 162–171]. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in [F....

An approximation theorem related to good compact sets in the sense of Martineau

Jean-Pierre Rosay, Edgar Lee Stout (2000)

Annales de l'institut Fourier

This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

An elementary proof of the Briançon-Skoda theorem

Jacob Sznajdman (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function φ belongs to an ideal I of the ring of germs of analytic functions at 0 ∈ ℂ n ; more precisely, the ideal membership is obtained if a function associated with φ and I is locally square integrable. If I can be generated by m elements,it follows in particular that I min ( m , n ) ¯ ⊂ I , where J ¯ denotes the integral closure of an ideal J .

An embedding relation for bounded mean oscillation on rectangles

Benoît F. Sehba (2014)

Annales Polonici Mathematici

In the two-parameter setting, we say a function belongs to the mean little BMO if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the present author in relation to the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space b m o ( N ) of functions of bounded mean oscillation is a strict subspace of the mean little BMO.

An energy estimate for the complex Monge-Ampère operator

Urban Cegrell, Leif Persson (1997)

Annales Polonici Mathematici

We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.

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 -∞.

Currently displaying 401 – 420 of 5576