The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type
Copyright policy )The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type
Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In [Chen Y., Its A., J. Approx. Theory 162 (2010), 270-297, arXiv:0808.3590] the authors proved that this deformation can be described by systems of differential/difference equations for the corresponding recursion coefficients and that these equations, ultimately, are equivalent to the Painlevé III equation and its Bäcklund/Schlesinger transformations. Here we prove that an analogue result holds for some kind of semiclassical matrix-valued orthogonal polynomials of Laguerre type.
- National Autonomous University of Mexico Mexico
- University of Angers France
Toda lattices, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, matrix-valued orthogonal polynomials, Riemann-Hilbert problems, FOS: Physical sciences, Painlevé equations, Mathematical Physics (math-ph), Isomonodromic deformations for ordinary differential equations in the complex domain, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematical Physics
Toda lattices, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, matrix-valued orthogonal polynomials, Riemann-Hilbert problems, FOS: Physical sciences, Painlevé equations, Mathematical Physics (math-ph), Isomonodromic deformations for ordinary differential equations in the complex domain, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematical Physics
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