Elenco seminari del ciclo di seminari
“SINGULAR DIFFERENTIAL OPERATORS WITH MEROMORPHIC EIGENFUNCTIONS”

These talks of P.G. Grinevich are based on joint works with S.P. Novikov and R.G. Novikov.
Ottobre
06
2017
P.G. Grinevich
Singular differential operators with meromorphic eigenfunctions - part II
nel ciclo di seminari: SINGULAR DIFFERENTIAL OPERATORS WITH MEROMORPHIC EIGENFUNCTIONS
analisi matematica
These two talks are based on joint works with S.P. Novikov and R.G. Novikov. Generically the spectral theory of differential operators with singular coefficients is badly defined. But following some ideas of soliton theory we consider a very special subclass of differential operators with meromoprphic coefficients such that: 1. In dimension 1 we assume that all eigenfunctions at all energy levels are meromorphic. 2. In dimension 2 we assume that at one energy level we have sufficiently many locally meromorphic solutions. We show that the spectral theory for such operators can be naturalyy defined, but the Hibert spaces of fucntions should be replaces by pseudo-Hilbert spaces of Potrjagin type. At the first talk we will focus on the 1-dimensinal case. In particular we show, that for such periodic operators the Bloch variety is well-defined. The second part will be dedicated to the 2-dimensional case.
organizzato da: Simonetta Abenda
nell'ambito del Progetto R.F.O. 2014 del prof. Alberto Parmeggiani
Ottobre
03
2017
P.G. Grinevich
Singular differential operators with meromorphic eigenfunctions - part I
nel ciclo di seminari: SINGULAR DIFFERENTIAL OPERATORS WITH MEROMORPHIC EIGENFUNCTIONS
analisi matematica
These two talks are based on joint works with S.P. Novikov and R.G. Novikov. Generically the spectral theory of differential operators with singular coefficients is badly defined. But following some ideas of soliton theory we consider a very special subclass of differential operators with meromoprphic coefficients such that: 1. In dimension 1 we assume that all eigenfunctions at all energy levels are meromorphic. 2. In dimension 2 we assume that at one energy level we have sufficiently many locally meromorphic solutions. We show that the spectral theory for such operators can be naturalyy defined, but the Hibert spaces of fucntions should be replaces by pseudo-Hilbert spaces of Potrjagin type. At the first talk we will focus on the 1-dimensinal case. In particular we show, that for such periodic operators the Bloch variety is well-defined. The second part will be dedicated to the 2-dimensional case.
organizzato da: Simonetta Abenda
nell'ambito del Progetto R.F.O. 2014 del prof. Alberto Parmeggiani