Abstract
As we had mentioned in the introduction the Schwartz approach to distribution theory defines distributions as continuous linear functions on a test function space. The various classes of distributions are distinguished by the underlying test function spaces. Before we come to the definition of the main classes of Schwartz distribution we collect some basic facts about continuous linear functions or functionals on a HLCTVS and about spaces of such functional. Then the definition of the three main spaces of Schwartz distributions is straightforward. Numerous examples explain this definition.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Blanchard, P., Brüning, E. (2003). Schwartz Distributions. In: Mathematical Methods in Physics. Progress in Mathematical Physics, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0049-9_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0049-9_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6589-4
Online ISBN: 978-1-4612-0049-9
eBook Packages: Springer Book Archive