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Spherical functions on ordered symmetric spaces

Jacques Faraut, Joachim Hilgert, Gestur Ólafsson (1994)

Annales de l'institut Fourier

We define on an ordered semi simple symmetric space ℳ = G / H a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when G is a complex group, H a real form of G , and when ℳ ...

Spherical Stein manifolds and the Weyl involution

Dmitri Akhiezer (2009)

Annales de l’institut Fourier

We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical subgroups...

Standard ideals in convolution Sobolev algebras on the half-line

José E. Galé, Antoni Wawrzyńczyk (2011)

Colloquium Mathematicae

We study the relation between standard ideals of the convolution Sobolev algebra ₊ ( n ) ( t ⁿ ) and the convolution Beurling algebra L¹((1+t)ⁿ) on the half-line (0,∞). In particular it is proved that all closed ideals in ₊ ( n ) ( t ⁿ ) with compact and countable hull are standard.

Stieltjes perfect semigroups are perfect

Torben Maack Bisgaard, Nobuhisa Sakakibara (2005)

Czechoslovak Mathematical Journal

An abelian * -semigroup S is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on S admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian * -semigroup S is perfect if for each s ∈ S there exist t ∈ S and m , n ∈ ℕ 0 such that m + n ≥ 2 ...

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