Let Kn be the Lorentz/second-order cone in IR. For any function f from IR to IR, one can define a corresponding vector-valued function f soc (x) on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity,...

Abstract Let ? be a proper open cone in real Banach space V . We show that the tube domain V ? i ? ? {V\oplus i\Omega} over is biholomorphic to bounded symmetric if and only normal linearly homogeneous Finsler cone, which equiva...

Let D = G/K be an irreducible Hermitian symmetric domain. ThenG is contained in a complexificationGC, and there exists a closed complex subsemigroup G ⊂ Γ ⊂ GC, the so-called minimal Ol’shanskĭı semigroup, characterised by the fact that all holomorphic discrete series representations of G extend holomorphically to Γ◦. Parallel to the classical theory of boundary strata for the symmetric domain ...

We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building otherwise. Furthermore, every boundary equivalence (cone topology homeomorphism preserving the Tits metric) between two such spaces is induced by a homothety. As an a...

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain V ⊕ iΩ that are obtained by analytic continuation of the holomorphic discrete series. For a representation corresponding to a discrete point in the Wallach set, we find the decomposition under restriction to the identity component of GL(Ω). Using Riesz distributions, an explicit int...

We focus on inverse preconditioners based on minimizing F(X) = 1− cos(XA, I), where XA is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F(X) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of...

Let D = G/K be an irreducible Hermitian symmetric domain. Then G is contained in a complexification GC, and there exists a closed complex subsemigroup G ⊂ Γ ⊂ GC characterised by fact that all holomorphic discrete series representations of G extend holomorphically to Γ◦, the socalled minimal Ol’shanskĭı semigroup. Parallel to the classical theory of boundary strata for the symmetric domain D, d...

In this paper, we consider tomographic reconstruction for axially symmetric objects from a single radiograph formed by fan-beam X-rays. All contemporary methods are based on the assumption that the density is piecewise constant or linear. From a practical viewpoint, this is quite a restrictive approximation. The method we propose is based on high-order total variation regularization. Its main a...

Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araújo & Stoeger (1999), their formulation and solution in the perturbed FLRW spherically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importanc...