Skip to main content

The theory of holonomic systems with regular singularities and its relevance to physical problems

  • Part I Microfunctions, Microlocal Calculus and Related Topics
  • Conference paper
  • First Online:
Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 126))

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bony, J. M. and P. Schapira: Propagation des singularité analytiques pour les solutions des équations aux dérivées partielles. Ann. Inst. Fourier, Grenoble, 26, 81–140 (1976).

    Google Scholar 

  2. Deligne, P.: Equations differentielles à points singuliers réguliers. Lecture Notes in Math. No.163, Berlin-Heidelberg-New York: Springer, 1970.

    Google Scholar 

  3. Iagolnitzer, D.: The u=0 structure theorem. Commun. math. Phys., 63, 49–96 (1978).

    Google Scholar 

  4. Kashiwara, M.: On the maximally overdetermined system of linear differential equations, I. Publ. RIMS, Kyoto Univ., 10, 563–579 (1975).

    Google Scholar 

  5. —: On the holonomic systems of linear differential equations. II. Inventiones math., 49, 121–135 (1978).

    Article  Google Scholar 

  6. Kashiwara, M. and T. Kawai: Micro-hyperbolic pseudo-differential operators I. J. Math. Soc. Japan, 27, 359–404 (1975).

    Google Scholar 

  7. —: Micro-local properties of \(\mathop \Pi \limits_{j = 1}^n f_{j^ + }^{S_j } \). Proc. Japan Acad., 51, 270–272 (1975).

    Google Scholar 

  8. —: Finiteness theorem for holonomic systems of micro-differential equations. Proc. Japan Acad., 52, 341–343 (1976).

    Google Scholar 

  9. —: Holonomic character and local monodromy structure of Feynman integrals. Commun. math. Phys., 54, 121–134 (1977).

    Article  Google Scholar 

  10. —: Holonomic systems of linear differential equations and Feynman integrals. Publ. RIMS, Kyoto Univ., 12 Suppl., 131–140 (1977).

    Google Scholar 

  11. —: On the characteristic variety of a holonomic system with regular singularities. Adv. in Math, 34, 163–184 (1979).

    Article  Google Scholar 

  12. —: On holonomic systems of micro-differential equations. III —Systems with regular singularities—. To appear. (RIMS Preprint No.293.)

    Google Scholar 

  13. Kashiwara, M., T. Kawai and T. Oshima: A study of Feynman integrals by micro-differential equations. Commun. math. Phys., 60, 97–130 (1978).

    Article  Google Scholar 

  14. Kashiwara, M., T. Kawai and H. P. Stapp: Micro-analyticity of the S-matrix and related functions. Commun. math. Phys., 66, 95–130 (1979).

    Article  Google Scholar 

  15. Kawai, T. and H. P. Stapp: Discountinuity formula and Sato's conjecture. Publ. RIMS, Kyoto Univ., 12 Suppl., 155–232 (1977).

    Google Scholar 

  16. Malgrange, B.: Sur les points singuliers des équations — differentielles. Enseignement Math. 20, 147–176 (1974).

    Google Scholar 

  17. Mebkhout, Z.: Local cohomology of analytic spaces. Publ. RIMS, Kyoto Univ., 12 Suppl., 247–256 (1977).

    Google Scholar 

  18. Oshima, T.: Singularities in contact geometry and degenerate pseudo-differential equations. J. Fac. Sci. Univ. Tokyo, IA, 21, 43–83 (1974).

    Google Scholar 

  19. Ramis, J. P.: Variations sur le theme “GAGA”. Lecture Notes in Math. No.694, pp.228–289, Berlin-Heidelberg-New York: Springer, 1978.

    Google Scholar 

  20. Sato, M.: Recent development in hyperfunction theory and its application to physics. Lecture Notes in Phys. No.39, pp. 36–48, Berlin-Heidelberg-New York: Springer, 1975.

    Google Scholar 

  21. Sato, M., T. Kawai and M. Kashiwara: Microfunctions and pseudo-differential equations. Lecture Notes in Math. No.287, pp. 265–529. Berlin-Heidelberg-New York: Springer, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

D. Iagolnitzer

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Kashiwara, M., Kawai, T. (1980). The theory of holonomic systems with regular singularities and its relevance to physical problems. In: Iagolnitzer, D. (eds) Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory. Lecture Notes in Physics, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09996-4_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-09996-4_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09996-3

  • Online ISBN: 978-3-540-39306-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics