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- Title
Commuting Ordinary Differential Operators with Polynomial Coefficients and Automorphisms of the First Weyl Algebra.
- Authors
Mironov, Andrey E.; Zheglov, Alexander B.
- Abstract
In this paper, we study rank 2 commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral curve of genus one the space of orbits is infinite. Moreover, we prove in this case that for any n≥1 there is a pair of self-adjoint commuting ordinary differential operators of rank 2 L4=(∂2x+V(x))2+W(x), L6, where W(x),V(x) are polynomials of degree n and n+2. We also prove that there are hyperelliptic spectral curves with the infinite spaces of orbits.
- Subjects
DIFFERENTIAL operators; POLYNOMIAL approximation; COEFFICIENTS (Statistics); AUTOMORPHISMS; LOGICAL prediction
- Publication
IMRN: International Mathematics Research Notices, 2016, Vol 2016, Issue 10, p2974
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnv218