The boson–fermion correspondence from linear ODEs

Notes on Linear Odes

Remark 1.3. Suppose the characteristic polynomial is given by χA(λ) = Π m i=1(λ−λi) , where λi are distinct. Then the polynomials p`,j(t) have degree strictly smaller than νj (Exercise: Why?) If A is real, we want to find an expression for general real solutions. These are in particular the solutions one obtain when given real initial data. Before we proceed, let us just make a simple observati...

Linear ODEs in Lie groups

The solution of Y 0 = A(t)Y; Y (0) = Y0, where Y is in a matrical Lie group G and A(t) is in the Lie algebra of G, is discussed in this article. The basis of our approach are generalized iterated commutators. In that manner we can approximate the solution to an arbitrarily high order. The exact solution is given as an infinite series of commutators and order conditions are studied by using bina...

Improved Multi overing Bounds from Linear Inequalities and Super odes

Generalized phase-integrals for linear homogeneous ODEs

Using a surprising result for the Wronskian of solutions with a common factor we show that all of the linearly independent solutions of linear-homogeneous ODEs have a simple form in a generalized phase-integral representation. This allows the generalization of WKB-like expansions to higher-order differential equations in a way that extends the usual phase-integral methods. This work clarifies t...

Robust Stability for Parametric Linear ODEs

Content: A logical tool in robust control theory for systems of parametric inhomogeneous linear ODEs.