Moebius-invariant algebras in balls

Moebius-Invariant Natural Neighbor Interpolation

We propose an interpolation method that is invariant under Möbius transformations; that is, interpolation followed by transformation gives the same result as transformation followed by interpolation. The method uses natural (Delaunay) neighbors, but weights neighbors according to angles formed by Delaunay circles.

Invariant Cubature Formulae for Spheres and Balls

Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T d. These formulae are used to derive cubature formulae on the surface of the sphere Sd and on the unit ball Bd using connections between cubature for...

Differential Invariant Algebras

The equivariant method of moving frames provides a systematic, algorithmic procedure for determining and analyzing the structure of algebras of differential invariants for both finite-dimensional Lie groups and infinite-dimensional Lie pseudo-groups. This paper surveys recent developments, including a few surprises and several open questions.

Topologically Left Invariant Mean on Dual Semigroup Algebras

Classification of Invariant Cones in Lie Algebras

We shall describe invariant cones in Lie algebras completely. For simple Lie algebras see [KR82, 0181, Pa84, and Vi80]. Some observations are simple: If W is an invariant cone in a Lie algebra g, then the edge e = W Pi — W and the span W — W are ideals. Therefore, if one aims for a theory without restriction on the algebra g it is no serious loss of generality to assume that W is generating, th...