Oscillation theory and semibounded canonical systems

2018/11/17 by Remling, Christian, Scarbrough, Kyle
#34C10 34L40 47A06 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1811.07067

Abstract

Oscillation theory locates the spectrum of a differential equation by counting the zeros of its solutions. We present a version of this theory for canonical systems Ju'=-zHu and then use it to discuss semibounded operators from this point of view. Our main new result is a characterization of systems with purely discrete spectrum in terms of the asymptotics of their coefficient functions; we also discuss the exponential types of the transfer matrices.

Related

• The essential spectrum of canonical systems
• Systems of linear ordinary differential equations with bounded coefficients may have very oscillating solutions
• Spectral properties of canonical systems: discreteness and distribution of eigenvalues
• Canonical systems with discrete spectrum
• Spectral theory of dynamical systems