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[[もとpage>ochiai/pv]] - Hideyuki Ishi, --Analysis on regular convex cones associated to decomposable graphs. --Regular convex cones of positive definite real symmetric matrices with prescribed zero entries have been studied intensively in multivariate statistics. It turned out that analysis on the cone is quite feasible if the zero pattern corresponds to a decomposable graph. Indeed, an explicit formula is known for the Fourier-Laplace transform of a product of powers of minors over the cone. Inspired by these statistic works, we develop analysis on the cone in a similar way to theory of homogeneous cones. In particular, we consider Riesz distributions on the cone and associated b-functions. -Yumiko Hironaka --Spherical functions on certain $p$-adic homogeneous spaces, and their relation to PV-theory
