Quasi-hierarchical Powell-Sabin splines are C-continuous quadratic splines defined on a locally refined hierarchical triangulation. They admit a compact representation in a normalized B-spline basis. We prove that the quasi-hierarchical basis is in general weakly Lpstable, but for a broad class of hierarchical triangulations it is even strongly Lp-stable.

Given a real-analytic Riemannian manifold M there exists a canonical complex structure on part of its tangent bundle which turns leaves of the Riemannian foliation on TM into holomorphic curves. A Grauert tube over M of radius r, denoted as T rM , is the collection of tangent vectors of M of length less than r equipped with this canonical complex structure. We say the Grauert tube T rM is rigid...

We introduce a wide subclass F(X,ω) of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well-defined and the convergence theorem is valid. We also prove that F(X,ω) is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.

Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the group is compact this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is non-compact the group averagin...

In this paper, we prove that for a noetherian formal scheme X, its derived category of sheaves of modules with quasi-coherent torsion homologies Dqct(X) is generated by a single compact object. In an appendix we prove that the category of compact objects in Dqct(X) is skeletally small.

Some curvature estimates are derived from geometrical data concerning quasi-conformality properties of some commuting linearly independent vector fields on a compact Riemannian manifold.