A Berezin-type map and a class of weighted composition operators
In this paper we consider the map L defined on the Bergman space [...] of the right half plane [...] .
A Borel-Weil theorem for holomorphic forms
A Characterization of Complex Homogeneous Cones.
A classification of strictly pseudoconcave homogeneous manifolds
A compactification of with no non-constant meromorphic functions
For each 2-dimensional complex torus , we construct a compact complex manifold with a -action, which compactifies such that the quotient of by the -action is biholomorphic to . For a general , we show that has no non-constant meromorphic functions.
A Contraction of S U (2) to the Heisenberg Group.
A description based on Schubert classes of cohomology of flag manifolds
We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.
A generalisation of Teichmüller space in the hermitian context
A Geometric Algebraicity Property for Moduli Spaces of Compact Kähler Manifolds with h 2, 0 = 1.
A geometric embedding for standard analytic modules.
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A KAM phenomenon for singular holomorphic vector fields
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection...
A local form for the automorphisms of the spectral unit ball.
A method for weight multiplicity computation based on Berezin quantization.
A Note on Coherent G-Sheaves.
A propos d'une conjecture de R. Hartshorne.
A Riemann Mapping Theorem for Bounded Symmetric Domains in Complex Banach Spaces.
A splitting criterion for two-dimensional semi-tori.
A weighted Plancherel formula II. The case of the ball
The group SU(1,d) acts naturally on the Hilbert space , where B is the unit ball of and the weighted measure . It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic...
A weighted Plancherel formula. III. The case of the hyperbolic matrix ball.