Normal forms of ordinary linear differential equations in arbitrary characteristic

07/04/2023

∙

Fuchs' Theorem on the solutions of ordinary linear differential equations with regular singularities is extended to positive characteristic by proving a normal form theorem for the respective linear differential operators. This yields an explicit algorithm to compute a basis of solutions in characteristic p.

READ FULL TEXT

Normal forms of ordinary linear differential equations in arbitrary characteristic

The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry

Factoring differential operators over algebraic curves in positive characteristic

Learning port-Hamiltonian systems – algorithms

Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations

Computation of the Similarity Class of the p-Curvature

Extremal Growth of Multiple Toeplitz Operators and Implications for Numerical Stability of Approximation Schemes

Universal Approximation Property of Neural Ordinary Differential Equations

Normal forms of ordinary linear differential equations in arbitrary characteristic

Related Research

The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry

Factoring differential operators over algebraic curves in positive characteristic

Learning port-Hamiltonian systems – algorithms

Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations

Computation of the Similarity Class of the p-Curvature

Extremal Growth of Multiple Toeplitz Operators and Implications for Numerical Stability of Approximation Schemes

Universal Approximation Property of Neural Ordinary Differential Equations