Skip to main content
Log in

Calculation of local formal Fourier transforms

  • Published:
Arkiv för Matematik

Abstract

We calculate the local Fourier transforms for connections on the formal punctured disk, reproducing the results of J. Fang and C. Sabbah using a different method. Our method is similar to Fang’s, but more direct.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Arinkin, A., Fourier transform and middle convolution for irregular \(\mathcal{D}\)-modules, Preprint, 2008. arXiv:0808.0699.

  2. Babbit, D. G. and Varadarajan, V. S., Local moduli for meromorphic differential equations, Astérisque 169–170 (1989), 1–217.

    Google Scholar 

  3. Beilinson, A., Bloch, S. and Esnault, H., ϵ-factors for Gauss–Manin determinants, Mosc. Math. J. 2 (2004), 477–532.

    MathSciNet  Google Scholar 

  4. Bloch, S. and Esnault, H., Local Fourier transforms and rigidity for \(\mathcal{D}\)-modules, Asian J. Math. 8 (2004), 587–605.

    MathSciNet  MATH  Google Scholar 

  5. Fang, J., Calculation of local Fourier transforms for formal connections, Preprint, 2007. arXiv:0707.0090.

  6. García López, R., Microlocalization and stationary phase, Asian J. Math. 8 (2004), 747–768.

    MathSciNet  MATH  Google Scholar 

  7. Levelt, A., Jordan decomposition for a class of singular differential operators, Ark. Mat. 13 (1975), 1–27.

    Article  MathSciNet  MATH  Google Scholar 

  8. Malgrange, B., Équations différentielles á coefficients polynomiaux, Progress in Math. 96, Birkhäuser, Boston, MA, 1991.

    MATH  Google Scholar 

  9. van der Put, M. and Singer, M., Galois Theory of Linear Differential Equations, Grundlehren der mathematischen Wissenschaften 328, Springer, Berlin–Heidelberg, 2003.

    Book  MATH  Google Scholar 

  10. Sabbah, C., An explicit stationary phase formula for the local formal Fourier–Laplace transform, Preprint, 2007. arXiv:0706.3570.

  11. Turrittin, H. L., Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point, Acta Math. 93 (1955), 27–66.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adam Graham-Squire.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Graham-Squire, A. Calculation of local formal Fourier transforms. Ark Mat 51, 71–84 (2013). https://doi.org/10.1007/s11512-011-0156-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11512-011-0156-2

Keywords

Navigation