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.
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© 2011 Springer Basel AG
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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
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DOI: https://doi.org/10.1007/978-3-7643-9992-4_14
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Publisher Name: Springer, Basel
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Online ISBN: 978-3-7643-9992-4
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