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Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case

Josef Janyška, Martin Markl (2012)

Archivum Mathematicum

This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.

Commutators of diffeomorphisms of a manifold with boundary

Tomasz Rybicki (1998)

Annales Polonici Mathematici

A well known theorem of Herman-Thurston states that the identity component of the group of diffeomorphisms of a boundaryless manifold is perfect and simple. We generalize this result to manifolds with boundary. Remarks on C r -diffeomorphisms are included.

Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators

S. Dekel, G. Kerkyacharian, G. Kyriazis, P. Petrushev (2014)

Studia Mathematica

A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with...

Currently displaying 141 – 160 of 387