Ebook: Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai
- Tags: Integral Transforms Operational Calculus, Ordinary Differential Equations, Partial Differential Equations, Special Functions
- Year: 2008
- Publisher: Springer Tokyo
- Edition: 1
- Language: English
- pdf
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005.
Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas.
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. This dedication is made on the occasion of Professor Kawai's 60th birthday as a token of deep appreciation of the important contributions he has made to the field. Introductory notes on the scientific works of Professor Kawai are also included.
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005.
Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas.
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. This dedication is made on the occasion of Professor Kawai's 60th birthday as a token of deep appreciation of the important contributions he has made to the field. Introductory notes on the scientific works of Professor Kawai are also included.
Content:
Front Matter....Pages I-XVII
Front Matter....Pages 1-1
Publications of Professor Takahiro Kawai....Pages 3-9
The work of T. Kawai on hyperfunction theory and microlocal analysis....Pages 11-13
The work of T. Kawai on hyperfunction theory and microlocal analysis....Pages 15-17
The work of T. Kawai on exact WKB analysis....Pages 19-25
Front Matter....Pages 27-27
Virtual turning points — A gift of microlocal analysis to the exact WKB analysis....Pages 29-43
Regular sequences associated with the Noumi-Yamada equations with a large parameter....Pages 45-53
Ghost busting: Making sense of non-Hermitian Hamiltonians....Pages 55-66
Vanishing of the logarithmic trace of generalized Szeg? projectors....Pages 67-78
Nonlinear Stokes phenomena in first or second order differential equations....Pages 79-87
Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation....Pages 89-99
Exact WKB analysis near a simple turning point....Pages 101-117
The Borel transform....Pages 119-131
On the use of Z-transforms in the summation of transseries for partial differential equations....Pages 133-141
Some dynamical aspects of Painlev? VI....Pages 143-156
An algebraic representation for correlation functions in integrable spin chains....Pages 157-166
Inverse image of D-modules and quasi-b-functions....Pages 167-177
The hypoelliptic Laplacian of J.-M. Bismut....Pages 179-194
Commuting differential operators with regular singularities....Pages 195-224
The behaviors of singular solutions of some partial differential equations in the complex domain....Pages 225-235
Observations on the JWKB treatment of the quadratic barrier....Pages 237-250
Front Matter....Pages 27-27
A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum H?non map....Pages 251-264
Spectral instability for non-selfadjoint operators....Pages 265-273
Boundary and lens rigidity, tensor tomography and analytic microlocal analysis....Pages 275-293
Coupling of two partial differential equations and its application....Pages 295-306
Instanton-type formal solutions for the first Painlev? hierarchy....Pages 307-319
From exact-WKB toward singular quantum perturbation theory II....Pages 321-334
WKB analysis and Poincar? theorem for vector fields....Pages 335-352
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005.
Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas.
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. This dedication is made on the occasion of Professor Kawai's 60th birthday as a token of deep appreciation of the important contributions he has made to the field. Introductory notes on the scientific works of Professor Kawai are also included.
Content:
Front Matter....Pages I-XVII
Front Matter....Pages 1-1
Publications of Professor Takahiro Kawai....Pages 3-9
The work of T. Kawai on hyperfunction theory and microlocal analysis....Pages 11-13
The work of T. Kawai on hyperfunction theory and microlocal analysis....Pages 15-17
The work of T. Kawai on exact WKB analysis....Pages 19-25
Front Matter....Pages 27-27
Virtual turning points — A gift of microlocal analysis to the exact WKB analysis....Pages 29-43
Regular sequences associated with the Noumi-Yamada equations with a large parameter....Pages 45-53
Ghost busting: Making sense of non-Hermitian Hamiltonians....Pages 55-66
Vanishing of the logarithmic trace of generalized Szeg? projectors....Pages 67-78
Nonlinear Stokes phenomena in first or second order differential equations....Pages 79-87
Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation....Pages 89-99
Exact WKB analysis near a simple turning point....Pages 101-117
The Borel transform....Pages 119-131
On the use of Z-transforms in the summation of transseries for partial differential equations....Pages 133-141
Some dynamical aspects of Painlev? VI....Pages 143-156
An algebraic representation for correlation functions in integrable spin chains....Pages 157-166
Inverse image of D-modules and quasi-b-functions....Pages 167-177
The hypoelliptic Laplacian of J.-M. Bismut....Pages 179-194
Commuting differential operators with regular singularities....Pages 195-224
The behaviors of singular solutions of some partial differential equations in the complex domain....Pages 225-235
Observations on the JWKB treatment of the quadratic barrier....Pages 237-250
Front Matter....Pages 27-27
A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum H?non map....Pages 251-264
Spectral instability for non-selfadjoint operators....Pages 265-273
Boundary and lens rigidity, tensor tomography and analytic microlocal analysis....Pages 275-293
Coupling of two partial differential equations and its application....Pages 295-306
Instanton-type formal solutions for the first Painlev? hierarchy....Pages 307-319
From exact-WKB toward singular quantum perturbation theory II....Pages 321-334
WKB analysis and Poincar? theorem for vector fields....Pages 335-352
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