Скачать с ютуб Davide Guzzetti (SISSA, Trieste, IT) в хорошем качестве

Davide Guzzetti (SISSA, Trieste, IT)

Title: Uniqueness of Asymptotic solutions for linear ODEs with not necessarily meromorphic coefficients - a Levinson type theorem. Abstract: We consider systems of linear ODEs with analytic coefficients on sectorial domains, which are asymptotically diagonal for large values of the independent variable z. Under some conditions, we show the existence and uniqueness of an asymptotic fundamental matrix solution on a big sectorial domain. This includes systems depending on parameters. The theorem is of Levinson type, but while Levinson's approach only predicts existence, we also establish uniqueness.The result applies to systems of ODEs with not necessarily meromorphic coefficients, the leading diagonal term of the matrix coefficient being a generalized polynomial in z with real exponents (equations arising ODE/IM correspondence are of this kind). Another application is the classical case of ODEs with meromorphic coefficients at a ramified singularity, for which we provide sufficient conditions to guarantee the uniqueness of a fundamental solution with prescribed asymptotics, and we explicitly characterize the optimal sector. This is a joint work with G. Cotti and D. Masoero (https://arxiv.org/pdf/2310.19739).