Microlocal WKB Expansions

Microlocal WKB expansions

Virtual Turning Points — A gift of microlocal analysis to the exact WKB analysis ?

School of Science and Engineering, Kinki University, Higashi-Osaka 577-8502, Japan Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502 Japan Hitachi Ltd., Asagaya-kita 2-13-2,...

Binary Trees, Left and Right Paths, WKB Expansions, and Painleve Transcendents

During the 10th Seminar on Analysis of Algorithms, MSRI, Berkeley, June 2004, Knuth posed the problem of analyzing the left and the right path length in a random binary trees. In particular, Knuth asked about properties of the generating function of the joint distribution of the left and the right path lengths. In this paper, we mostly focus on the asymptotic properties of the distribution of t...

Microlocal Studies of Shapes

A gentle introduction to stratified Morse theory and Kashiwara’s conormal cycle.

Microlocal Analysis in Tomography

In this chapter, we introduce a range of tomography problems, including Xray imaging, limited data problems, electron microscopy and radar imaging. We are interested in the recovery of the singular features of the medium or object rather than exact inversion formulas. Toward this end, we show how microlocal analysis helps researchers understand the strengths and limitations inherent in the reco...