Fractional Calculus of Weyl Algebra and Fuchsian Differential Equations

Name: Fractional Calculus of Weyl Algebra and Fuchsian Differential Equations
Brand: Mathematical Society of Japan
Availability: OutOfStock
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By Toshio Oshima

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Description

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.

Product details

Binding:: Paperback
Edition:: 1
Number of Pages:: 203
Release Date:: 2012-11-01
Publication Date:: 2012-11-01
Publisher:: Mathematical Society of Japan
Languages:: Original: English
ISBN10:: 4864970165
ISBN13:: 9784864970167
Weight:: 415 g
Height:: 24.1 cm
Width:: 17.7 cm
Thickness:: 1.2 cm

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