55 research outputs found

    Holomorphic horospherical duality "sphere-cone"

    Get PDF
    We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.Comment: 9 page

    Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

    Full text link
    In this paper we define a distinguished boundary for the complex crowns \Xi\subeq G_\C /K_\C of non-compact Riemannian symmetric spaces G/KG/K. The basic result is that affine symmetric spaces of GG can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.Comment: 29 page

    Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem

    Full text link
    We prove a complex version of Kostant's non-linear convexity theorem. Applications to the construction of G-invariant Grauert tubes of non-compact Riemannian symmetric G/K spaces are given.Comment: 9 page

    Holomorphic horospherical transform on non-compactly causal spaces

    Full text link
    We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.Comment: Revised, final version; to appear in IMRN, 38

    HOROSPHERICAL CAUCHY TRANSFORM ON QUADRICS

    Get PDF
    Abstract. We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics I believe that the connection of harmonic analysis and complex analysis has an universal character and is not restricted by the case of complex homogeneous manifolds. It looks as a surprise that such a connection exists and though it is quite natural for finite dimensional representations and compact Lie groups [Gi00,Gi02]. In this note we describe the complex picture which corresponds to harmonic analysis on the real sphere. The basic construction is a version of horospherical transform which in this case is a holomorphic integral transform between holomorphic functions on the complex sphere and the complex spherical cone. This situation looks quite unusual from the point of view of complex analysis and I believe presents a serious interest also in this setting. It can be considered as a version of the Penrose transform), but in a purely holomorphic situation when there is neither cohomology nor complex cycles
    corecore