Formal factorization of higher order irregular linear differential operators
| Autor: | Leanne Mezuman, Sergei Yakovenko |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Weyl algebra
Pure mathematics Mathematics - Complex Variables General Mathematics Laurent series Order (ring theory) Field (mathematics) Differential operator Factorization Mathematics - Classical Analysis and ODEs Ordinary differential equation Classical Analysis and ODEs (math.CA) FOS: Mathematics Complex Variables (math.CV) Commutative property Mathematics |
| DOI: | 10.48550/arxiv.1805.02210 |
| Popis: | We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solution (given in terms of the Newton diagram and the respective characteristic numbers) is known for quite some time, though the proofs are rather involved. We suggest a process of reduction of the non-commutative problem to its commutative analog, the problem of factorization of pseudopolynomials, which is known since Newton invented his method of rotating ruler. It turns out that there is an "automatic translation" which allows to obtain the results for formal factorization in the Weyl algebra from well known results in local analytic geometry. Besides, we draw some (apparently unnoticed) parallelism between the formal factorization of linear operators and formal diagonalization of systems of linear first order differential equations. Comment: 17 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|