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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/1312
- Title
- How to use Fourier transform in asymptotic analysis
- Author(s)
- Gurarii, V.; Steiner, J.; Katsnelson, V.; Matsaev, V.
- Abstract
- This introductory paper presents a method for the analysis of differential equations with polynomial coefficients which also provides a funher insight into the Stokes Phenomenon. The method consists of a chain of steps based on the concept of the Stokes Structure and Fourier-like transforms adjusted to this Stokes Structure. Although the main object here is Bessel's equation our approach can be extended to more general matrix equations. It will be shown (i) how to derive the Stokes Structure directly from differential equations without any previous knowledge of Bessel or hypergeometric functions, (ii) how to adjust Fourier transforms to the Stokes Structure, (iii) how to answer questions on the interrelation between formal and actual solutions of Bessel's equation using Fourier Analysis, and finally (iv) how to evaluate the coefficient of the Stoke's Structure, thus providing a new insight into the Stokes Phenomenon.
- Publication type
- Book chapter
- Research centre
- Swinburne University of Technology. Centre for Mathematical Modelling
- Source
- Twentieth century harmonic analysis: a celebration / James S. Byrnes (ed.), pp. 387-401
- Publication year
- 2001
- Publisher
- Kluwer Academic Publishers
- ISBN
- 0792371690
- Copyright
- Copyright © 2001 Kluwer Academic Publishers.
- Peer reviewed
