Download Algebraic Analysis of Differential Equations: from by Takashi Aoki, Hideyuki Majima, Yoshitsugu Takei, Nobuyuki PDF

By Takashi Aoki, Hideyuki Majima, Yoshitsugu Takei, Nobuyuki Tose (eds.)

This quantity comprises 23 articles on algebraic research of differential equations and similar subject matters, so much of which have been offered as papers on the foreign convention "Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics" at Kyoto collage in 2005.

Microlocal research and exponential asymptotics are in detail hooked up and supply robust instruments which were utilized to linear and non-linear differential equations in addition to many similar fields comparable to genuine and complicated research, necessary transforms, spectral concept, inverse difficulties, integrable platforms, and mathematical physics. The articles contained the following current many new effects and ideas.

This quantity is devoted to Professor Takahiro Kawai, who's one of many creators of microlocal research and who brought the means of microlocal research into exponential asymptotics. This commitment is made at the get together of Professor Kawai's sixtieth birthday as a token of deep appreciation of the real contributions he has made to the sector. Introductory notes at the clinical works of Professor Kawai also are included.

Show description

Read Online or Download Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai PDF

Similar analysis books

Variational Analysis and Generalized Differentiation II. Applications

Variational research is a fruitful zone in arithmetic that, on one hand, bargains with the research of optimization and equilibrium difficulties and, however, applies optimization, perturbation, and approximation rules to the research of a vast variety of difficulties that won't be of a variational nature.

Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai

This quantity comprises 23 articles on algebraic research of differential equations and comparable issues, such a lot of that have been offered as papers on the foreign convention "Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics" at Kyoto collage in 2005.

Extra info for Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai

Example text

Then the following two conditions are equivalent: 1. The sequence f0 , f1 , . . , fl is a tame regular sequence at x0 . 2. For any k = 0, . . , l and for any (k + 1) choice fl0 , fl1 , . . , flk of elements in {f0 , f1 , . . , fl }, the dimension of V (x0 , fl0 , . . , flk ) is equal to n − k − 1 or V (x0 , fl0 , . . , flk ) is an empty set. Now let us study the relation between the notion of tame regular sequences and the Koszul complex. We denote by L· = K(f0 , f1 , . . , fl ; O) the Koszul complex associated with the sequence f0 , f1 , .

Shudo and Y. 53-63. 42 Takashi Aoki et al. [AKKT] [AKSST] [AKT1] [AKT2] [AKT3] [AKT4] [AKT5] [BW] [BNR] [CH] [DDP] [H] [Ho] [HLO] [KKNT] [KT] [NY] [P] [Sa1] [Sa2] T. Aoki, T. Kawai, T. Koike and Y. Takei: On global aspects of exact WKB analysis of operators admitting infinitely many phases. 373, 2005, pp. 11-47. T. Aoki, T. Kawai, S. Sasaki, A. Shudo and Y. Takei: Virtual turning points and bifurcation of Stokes curves, J. Phys. A: Math. , 38 (2005), 3317-3336. Takei: New turning points in the exact WKB analysis for higher-order ordinary differential equations, Analyse Alg´ebrique des Perturbations Singuli`eres.

As a matter of fact, using the following very simple third order equation d3 d + 2ixη 3 ψ = 0, + 3η 2 3 dx dx (10) Berk et al. pointed out in [BNR] that, in addition to ordinary Stokes curves, we need to introduce “new Stokes curves” to describe where Stokes phenomena for Borel resummed WKB solutions occur. A natural question then arises: What is a new Stokes curve? Bringing in the microlocal analysis to the study of singularities of Borel transformed WKB solutions, Kawai gave the following intriguing answer to the above question in [93]: Let P (x, ∂x , ∂y ) be the Borel transform of the operator P (x, ∂x , η) in question and take a self-intersection point of the bicharacteristic curve of P (x, ∂x , ∂y ).

Download PDF sample

Rated 4.58 of 5 – based on 17 votes
 

Author: admin