Let X be a complex projective manifold and let $$D\subset X$$ smooth divisor. In this article, we are interested in studying limits when $$\beta \rightarrow 0$$ of Kähler–Einstein metrics $$\omega _\beta $$ with cone singularity angle $$2\pi \beta along D. our first result, assume that $$X\setminus D$$ is locally symmetric space show converges to the metric further give asymptotics ball quotien...

In [7], Genkai Zhang gives the asymptotic expansion for the spherical functions on symmetric cones. This is done to prove a central limit theorem for these spaces. The work of Zhang is a natural continuation of the work of Audrey Terras [6] (the case of the positive definite matrices of rank 2) and of the work of Donald St.P. Richards [3] (the case of the positive definite matrices of all ranks...

Let Ω be a symmetric cone and V the corresponding simple Euclidean Jordan algebra. In [2, 5, 6, 8] we considered the family of generalized Laguerre functions on Ω that generalize the classical Laguerre functions on R. This family forms an orthogonal basis for the subspace of L-invariant functions in L(Ω, dμν), where dμν is a certain measure on the cone and where L is the group of linear transfo...

Abstract We prove the following result: Let K be a strictly convex body in Euclidean space ℝ n , ≥ 3, and let L hypersurface which is image of an embedding sphere

A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t → p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function of x, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, an...