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The Lie Group Structure of the Butcher Group
- Geir Bogfjellmo, Alexander Schmeding
- MathematicsFound. Comput. Math.
- 17 October 2014
TLDR
Extending Whitney’s extension theorem: nonlinear function spaces
- David Michael Roberts, Alexander Schmeding
- MathematicsAnnales de l'Institut Fourier
- 12 January 2018
This article shows that there is a continuous extension operator for compactly-supported smooth sections of vector bundles on possibly non-compact smooth manifolds, where the closed set to which…
The Lie group of bisections of a Lie groupoid
- Alexander Schmeding, Christoph Wockel
- Mathematics
- 4 September 2014
In this article, we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra…
Shape analysis on homogeneous spaces
- E. Celledoni, Sølve Eidnes, Alexander Schmeding
- Mathematics
- 5 April 2017
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare…
Shape Analysis on Homogeneous Spaces: A Generalised SRVT Framework
- E. Celledoni, Sølve Eidnes, Alexander Schmeding
- Mathematics
- 16 August 2016
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare…
Manifolds of absolutely continuous curves and the square root velocity framework
- Alexander Schmeding
- Mathematics
- 8 December 2016
A classical result in Riemannian geometry states that the absolutely continuous curves into a (finite-dimensional) Riemannian manifold form an infinite-dimensional manifold. In the present paper this…
Lie groupoids of mappings taking values in a Lie groupoid
- H. Amiri, Helge Glockner, Alexander Schmeding
- MathematicsArchivum Mathematicum
- 7 November 2018
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are…
The Lie group of real analytic diffeomorphisms is not real analytic
- R. Dahmen, Alexander Schmeding
- Mathematics
- 24 October 2014
We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it…
Differentiable mappings on products with different degrees of differentiability in the two factors
- Hamza Alzaareer, Alexander Schmeding
- Mathematics
- 31 August 2012
The tame Butcher group
- Geir Bogfjellmo, Alexander Schmeding
- Mathematics
- 11 September 2015
The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge--Kutta methods. Recently, a natural Lie group structure has been…
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