SG-classes, singular symplectic geoemtry, and order preserving isomorphisms

Research output: Thesis › Doctoral thesis

Authors

  • Alessandro Pietro Contini

Research Organisations

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Details

Original languageEnglish
QualificationDoctor rerum naturalium
Awarding Institution
Supervised by
  • Elmar Schrohe, Supervisor
Date of Award26 Jul 2023
Place of PublicationHannover
Publication statusPublished - 2023

Abstract

The geometric theory of pseudo-differential and Fourier Integral Operators relies on the symplectic structure of cotangent bundles. If one is to study calculi with some specific feature adapted to a geometric situation, the corresponding notion of cotangent bundle needs to be adapted as well and leads to spaces with a singular symplectic structure. Analysing these singularities is a necessary step in order to construct the calculus itself. In this thesis we provide some new insights into the symplectic structures arising from asymptotically Euclidean manifolds. In particular, we study the action of the Poisson bracket on SG-pseudo-differential operators and define a new class of singular symplectomorphisms, taking into account the geometric picture. We then consider this notion in the context of the characterisation of order-preserving isomorphisms of the SG-algebra, and show that these are in fact given by conjugation with a Fourier Integral Operator of SG-type.

Cite this

SG-classes, singular symplectic geoemtry, and order preserving isomorphisms. / Contini, Alessandro Pietro.
Hannover, 2023. 68 p.

Research output: Thesis › Doctoral thesis

Contini, AP 2023, 'SG-classes, singular symplectic geoemtry, and order preserving isomorphisms', Doctor rerum naturalium, Leibniz University Hannover, Hannover. https://doi.org/10.15488/15187
Contini, A. P. (2023). SG-classes, singular symplectic geoemtry, and order preserving isomorphisms. [Doctoral thesis, Leibniz University Hannover]. https://doi.org/10.15488/15187
Contini AP. SG-classes, singular symplectic geoemtry, and order preserving isomorphisms. Hannover, 2023. 68 p. doi: 10.15488/15187
Contini, Alessandro Pietro. / SG-classes, singular symplectic geoemtry, and order preserving isomorphisms. Hannover, 2023. 68 p.
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