Fractional calculus of Weyl algebra and Fuchsian differential equations / Toshio Oshima.

Oshima, Toshio [Browse]
Tokyo. : Mathematical Society of Japan, 2012.
1 online resource (xix, 203 pages) : illustrations.


Subseries of
Mathematical Society of Japan Memoirs
Summary note
Annotation In this book we give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The integral representations and series expansions of their solutions are also within our interpretation. As an application to Fuchsian differential equations on the Riemann sphere, we construct a universal model of Fuchsian differential equations with a given spectral type, in particular, we construct a single ordinary differential equation without apparent singularities corresponding to any rigid local system on the Riemann sphere, whose existence was an open problem presented by N. Katz.Furthermore we obtain fundamental properties of the solutions of the rigid Fuchsian differential equations such as their connection coefficients and the necessary and sufficient condition for the irreducibility of their monodromy groups. We give many examples calculated by our fractional calculus.Published by World Scientific Education and distributed by World Scientific Publishing Co. for all markets.
Source of description
Description based on publisher supplied metadata and other sources.
  • Fractional operations
  • Confluences
  • Series expansion and contiguity relation
  • Fuchsian differential equation and generalized Riemann scheme
  • Reduction of Fuchsian differential equations
  • Deligne-Simpson problem
  • A Kac-Moody root system
  • Expression of local solutions
  • Monodromy
  • Reducibility
  • Shift operators
  • Connection problem
  • Examples
  • Further problems.
Other title(s)
Fractional calculus of Weyl algebra and Fuchsian differential equations. Vol 28
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