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- Hideyuki Ishi
- 1999

Riesz distributions are relatively invariant distributions supported by the closure of a homogeneous cone . In this paper, we clarify the positivity condition of Riesz distributions by relating it to the orbit structure of . Moreover each of the positive Riesz distributions is described explicitly as a measure on an orbit in .

- Hideyuki Ishi
- GSI
- 2015

- Hideyuki Ishi
- 2001

In harmonic analysis on classical domains of matrices, the differential operator whose symbol is the determinant polynomial plays important roles. Particularly, the operator is substantial in study of invariant Hilbert spaces of holomorphic functions on the domain [1, 2, 7, 14, 15, 21]. Considering the Siegel domain realization of a certain symmetric domain… (More)

We introduce a natural definition of Riesz measures and Wishart laws associated to an Ω-positive (virtual) quadratic map, where Ω ⊂ Rn is a regular open convex cone. We give a general formula for moments of the Wishart laws. Moreover, if the quadratic map has an equivariance property under the action of a linear group acting on the cone Ω transitively, then… (More)

- Harald Upmeier, Alexander Alldridge, +14 authors Harald Upmeier
- 2006

Qp spaces on the unit disc were introduced, and their basic properties established, in 1995 by Aulaskari, Xiao and Zhao. Later some of these results were extended also to the unit ball or even to strictly pseudoconvex domains in the complex n-space. We briefly review the theory of bounded symmetric domains, of which the disc and the ball are the simplest… (More)

Introduction. Riesz distributions, originally introduced by M. Riesz [6] on the Lorentz cone, are the analytic continuation of the distribution defined by a relatively invariant measure on a homogeneous cone. In general, Riesz distributions are compositions of complex measures supported by the closure of the cone with differential operators. Gindikin [3]… (More)

- Hideyuki Ishi
- Entropy
- 2016

Abstract: The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an… (More)

- Hideyuki Ishi
- GSI
- 2017

- Hideyuki Ishi
- 2007

Let G be the split solvable Lie group acting simply transitively on a Siegel domain D. We consider irreducible unitary representations of G realized on Hilbert spaces of holomorphic functions on D. We determine all such Hilbert spaces by connecting them with positive Riesz distributions on the dual cone and describe them through the Fourier-Laplace… (More)

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