Gevrey WKB method for PDO's of real principal type
Richard Lascar, Ivan Moyano
TL;DR
This paper extends the WKB method to Gevrey class pseudodifferential operators of real principal type, introducing conjugation by FIOs and Gevrey FBI transforms, with subexponential remainders.
Contribution
It develops a Gevrey version of the WKB method for PDOs, including a calculus of FIOs and an alternative approach using Gevrey FBI transforms.
Findings
Established subexponential remainders in the Gevrey setting
Developed a calculus of FIOs for Gevrey PDOs
Proposed an alternative Gevrey FBI transform method
Abstract
In this article we investigate the Gevrey version of the WKB method known in the smooth and analytic categories. We use conjugation by FIO's and sketch a calculus of FIO's in our setting which the semi classic one. We have sub exponential remainders with respect to the parameter. We sketch also an alternative method using Gevrey local FBI transforms.
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Taxonomy
TopicsDigital Filter Design and Implementation · Advanced Electrical Measurement Techniques · Electromagnetic Simulation and Numerical Methods