Asymptotic solutions to Fuchsian equations in several variables

Boris Sternin; Victor Shatalov

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 351-363
  • ISSN: 0137-6934

Abstract

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The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.

How to cite

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Sternin, Boris, and Shatalov, Victor. "Asymptotic solutions to Fuchsian equations in several variables." Banach Center Publications 33.1 (1996): 351-363. <http://eudml.org/doc/262703>.

@article{Sternin1996,
abstract = {The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.},
author = {Sternin, Boris, Shatalov, Victor},
journal = {Banach Center Publications},
keywords = {Fuchsian equations; resurgent solutions},
language = {eng},
number = {1},
pages = {351-363},
title = {Asymptotic solutions to Fuchsian equations in several variables},
url = {http://eudml.org/doc/262703},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Sternin, Boris
AU - Shatalov, Victor
TI - Asymptotic solutions to Fuchsian equations in several variables
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 351
EP - 363
AB - The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.
LA - eng
KW - Fuchsian equations; resurgent solutions
UR - http://eudml.org/doc/262703
ER -

References

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  1. [1] B. Yu. Sternin and V. E. Shatalov, On a notion of resurgent function of several variables, Math. Nachr. 171 (1995), 283-301. Zbl0842.32006
  2. [2] M. Kashiwara and T. Kawai, Second microlocalization and asymptotic expansions, in: Lecture Notes in Phys. 126, Springer, New York, 1980, 21-76. 
  3. [3] R. Melrose, Analysis on Manifolds with Corners, Lecture Notes, MIT, Cambridge, Mass., 1988. 
  4. [4] B.-W. Schulze, Pseudodifferential Operators on Manifolds with Singularities, North-Holland, Amsterdam, 1991. 
  5. [5] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics. I, J. Differential Equations 101 (1993), 28-57. Zbl0777.47028
  6. [6] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics. II, in: Partial Differential Equations, Banach Center Publ. 27, Inst. of Math., Polish Acad. Sci., Warszawa, 1992, 555-580. Zbl0813.47061
  7. [7] B.-W. Schulze, B. Sternin and V. Shatalov, Resurgent analysis in the theory of differential equations with singularities, Math. Nachr. 170 (1994), 1-21. Zbl0847.35025
  8. [8] H. Komatsu, Laplace transform of hyperfunctions. A new foundation of Heaviside calculus, J. Fac. Sci. Univ. Tokyo IA 34 (1987), 805-820. Zbl0644.44001
  9. [9] B. Candelpergher, J. C. Nosmas and F. Pham, Approche de la Résurgence, Hermann, 1993. 
  10. [10] B. Yu. Sternin and V. E. Shatalov, Differential Equations on Complex Manifolds, Kluwer Acad. Publ., Dordrecht, 1994. Zbl0818.35003
  11. [11] B. Yu. Sternin and V. E. Shatalov, On a formula for the asymptotic expansion of an integral in complex analysis, Soviet Math. Dokl. 43 (1991), 624-627. Zbl0753.30027
  12. [12] B. Yu. Sternin and V. E. Shatalov, Stationary phase method for Laplace-Radon transformation, Mat. Zametki 51 (4) (1992), 116-125 (in Russian). 
  13. [13] B. Yu. Sternin and V. E. Shatalov, On exact asymptotics at infinity of solutions to differential equations, preprint, Max-Planck-Institut für Mathematik, Bonn, 1993. 
  14. [14] M. V. Korovina, B. Yu. Sternin and V. E. Shatalov, Asymptotical expansions 'in the large' of solutions of the complex Cauchy problem with singular initial data, Soviet Math. Dokl. 44 (1991), 674-677. Zbl0798.58076

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