Abstract
In the applications to quantum mechanics that we have in mind in this book a crucial role is played by non-local effects in symplectic space; for this reason the local theory traditionally developed by many authors working in the theory of partial differential equations is of little use. This chapter is a review of pseudo-differential calculus from the point of view developed in Shubin [147]. The specificity of this calculus is that the symbols satisfy global estimates where the x and p variables are placed on equal footing.
This is a preview of subscription content, log in via an institution to check access.
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
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Basel AG
About this chapter
Cite this chapter
de Gosson, M.A. (2011). Shubin’s Global Operator Calculus. In: Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Pseudo-Differential Operators, vol 7. Springer, Basel. https://doi.org/10.1007/978-3-7643-9992-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-7643-9992-4_14
Published:
Publisher Name: Springer, Basel
Print ISBN: 978-3-7643-9991-7
Online ISBN: 978-3-7643-9992-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)