Takaaki Nomura

Family of Cayley transforms of a homogeneous Siegel domain parametrized by admissible linear forms

In this paper we introduce a family of Cayley transforms of a homogeneous Siegel domain D. Each of these transforms is birational and maps D biholomorphically onto a bounded domain in a complex Euclidean vector space.

Berezin transforms and Laplace-Beltrami operators on homogeneous Siegel domains

Abstract In this paper we show that on a homogeneous Siegel domain, commutativity of Berezin transforms with the Laplace–Beltrami operator is equivalent to the symmetry of the domain

Grassmann manifold of aJH-algebra

We study the set of rankp idempotents in a topologically simple Hilbert Jordan algebra (JH-algebra for short). To produce the differential geometric structure on, we establish Jordan algebraic results concerning the structure of some two-generator subalgebras. We identify geodesics, the Riemannian distance and the sectional curvature of by using the Jordan algebraic structure.

Geometric norm equality related to the harmonicity of the Poisson kernel for homogeneous Siegel domains

In this paper, we present a geometric norm equality involving an admissible linear form ω for the Shilov boundary of a homogeneous Siegel domain D. We prove that the validity of this norm equality is equivalent to the symmetry of D and the reduction of ω essentially to the Koszul form. This, in particular, reveals a geometric reason that the Poisson kernel is annihilated by the Laplace–Beltrami operator if and only if D is symmetric, a theorem due to Hua, Look, Koranyi and Xu.

A characterization of symmetric Siegel domains through a Cayley transform

In this paper we give a characterization of symmetric Siegel domains in terms of a certain norm equality which involves a Cayley transform.

Geometric and harmonic analysis on homogeneous spaces

Lunch 15:00 −− 15:50 M. Benammar (Sfax) Deformation of sl(2) and osp(1|2)-Modules of Symbols. 16:00 −− 16:50 Ratnakumar P.K. (Allahabad) Non linear Schrodinger equation and the special hermite operator. 17:00 −− 17:30 Co ee break 17:30 −− 18:00 Parallel sessions of 30 minutes. 17:30 −− 18:00 S. Azaouzi (Sfax) A generalized analogue of Hardys uncertainty principle on compact extensions of R. 17:30 −− 18:00 M. Akriche (Monastir) Real algebraic surfaces bered in curves of genus 2 (The classi cation of singular bers).

Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action

In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2,ℂ) of complex 2×2 matrices related to the two-sided action ofU(2)×U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation ofGL(2,ℂ) and each eigenvalue is expressed as a finite sum involving the MeijerG-functions evaluated at 1 and the Hahn polynomials.

A description of a space of holomorphic discrete series by means of the Fourier transform on the Šilov boundary

Abstract Realizing holomorphic discrete series representations on Hilbert spaces H (Λ) of vector valued holomorphic functions on a Siegel domain of type II, we establish a Paley-Wiener type theorem for H (Λ) analogous to the classical one for Hardy space on the upper half plane.