Middle Convolution and Heun's Equation

Abstract

Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlevé equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.

References in corpus (6)

• Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlevé equation of type VI, Part I
• The Heun equation and the Calogero-Moser-Sutherland system II: perturbation and algebraic solution
• Complex Periodic Potentials with a Finite Number of Band Gaps
• Integral representation of solutions to Fuchsian system and Heun's equation
• Painlevé equations and the middle convolution
• Schlesinger transformations for algebraic Painleve VI solutions

Cited by in corpus (8)

• Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations
• Integral transformation of Heun's equation and some applications
• $q$-Middle Convolution and $q$-Painlevé Equation
• The geometry of generalized Lame equation, III: One-to-one of the Riemann-Hilbert correspondence
• Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
• Resolving singularities and monodromy reduction of Fuchsian connections
• q-Heun equation and initial-value space of q-Painlevé equation
• Solutions of Darboux Equations, its Degeneration and Painlevé VI Equations