Analytic geometry and semi-classical analysis

Analytic Geometry and Semi-classical Analysis

We study deformation theory for quantum integrable systems and prove several theorems concerning the Gevrey convergence and the unicity of perturbative expansions. À V.I. Arnold pour ses 70 ans.

Spectral Geometry and the Semi-classical Approach

Semi-Analytic Geometry with R-Functions

V. L. Rvachev called R-functions “logically-charged functions” because they encode complete logical information within the standard setting of real analysis. He invented them in the 1960s as a means for unifying logic, geometry, and analysis within a common computational framework – in an effort to develop a new computationally effective language for modeling and solving boundary value problems...

Semi-classical analysis

3 4 CONTENTS 2.2.2 The space of fixed vectors for a compact group is sym

Semi-classical Analysis and Pseudospectra

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit. AMS subject classification numbers: 81Q20, 47Axx, 34Lxx.