Shubin’s Global Operator Calculus

Part of the Pseudo-Differential Operators book series (PDO, volume 7)


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.


Asymptotic Expansion Inverse Fourier Transform Fourier Integral Operator Symplectic Space Symbol Class 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics, NuHAGUniversity of ViennaViennaAustria

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