Algebraic Analysis of Differential Equations

from Microlocal Analysis to Exponential Asymptotics

By: T. Aoki (Editor), H. Majima (Editor), Y. Takei (Editor)

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Hardcover | 16 November 2007

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374 Pages

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This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations - from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Functional Analysis & Transforms Algebra Integral Calculus & Equations

Publications of Professor Takahiro Kawai	p. 3
The work of T. Kawai on hyperfunction theory and microlocal analysis, part 1 - microlocal analysis and differential equations	p. 11
The work of T. Kawai on hyperfunction theory and microlocal analysis, part 2 - operators of infinite order and convolution equations	p. 15
The work of T. Kawai on exact WKB analysis	p. 19
Virtual turning points - a gift of microlocal analysis to the exact WKB analysis	p. 29
Regular sequences associated with the Noumi-Yamada equations with a large parameter	p. 45
Ghost busting : making sense of non-Hermitian Hamiltonians	p. 55
Vanishing of the logarithmic trace of generalized Szego projectors	p. 67
Nonlinear Stokes phenomena in first or second order differential equations	p. 79
Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation	p. 89
Exact WKB analysis near a simple turning point	p. 101
The Borel transform	p. 119
On the use of Z-transforms in the summation of transseries for partial differential equations	p. 133
Some dynamical aspects of Painleve VI	p. 143
An algebraic representation for correlation functions in integrable spin chains	p. 157
Inverse image of D-modules and quasi-bu-functions	p. 167
The hypoelliptic Laplacian of J.-M. Bismut	p. 179
Commuting differential operators with regular singularities	p. 195
The behaviors of singular solutions of some partial differential equations in the complex domain	p. 225
Observations on the JWKB treatment of the quadratic barrier	p. 237
A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Henon map	p. 251
Spectral instability for non-selfadjoint operators	p. 265
Boundary and lens rigidity, tensor tomography and analytic microlocal analysis	p. 275
Coupling of two partial differential equations and its application	p. 295
Instanton-type formal solutions for the first Painleve hierarchy	p. 307
From exact-WKB toward singular quantum perturbation theory II	p. 321
WKB analysis and Poincare theorem for vector fields	p. 335
Table of Contents provided by Blackwell. All Rights Reserved.

Algebraic Analysis of Differential Equations

from Microlocal Analysis to Exponential Asymptotics

At a Glance

Hardcover

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