Abstract
This chapter is devoted to some aspects of distribution theory. In Section 1.1 we define various spaces of smooth functions as well as some differential operators; we insist on an invariant definition of these objects, since this will be important in the study of N-body Hamiltonians. Various definitions and facts from distribution theory are reviewed in Section 1.2. The reader should be familiar with the contents of these two sections because we fix notations and terminology which are in some cases not quite standard. Sections 1.3 and 1.4 are more technical and may be skipped temporarily. We prove results relating local regularity properties of a distribution with the behaviour at infinity of its Fourier transform. We also establish an identity due to A.P. Calderón giving a representation of a distribution in terms of its derivatives of a fixed order plus a regular term. Finally, we use this representation in order to prove several facts that will be needed in later chapters.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Basel AG
About this chapter
Cite this chapter
Amrein, W.O., de Monvel, A.B., Georgescu, V. (1996). Some Spaces of Functions and Distributions. In: C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Progress in Mathematics, vol 135. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7762-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7762-6_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7764-0
Online ISBN: 978-3-0348-7762-6
eBook Packages: Springer Book Archive