Oscillation theory and semibounded canonical systems
Christian Remling
University of Oklahoma, Norman, USAKyle Scarbrough
University of Oklahoma, Norman, USA
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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 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.
Cite this article
Christian Remling, Kyle Scarbrough, Oscillation theory and semibounded canonical systems. J. Spectr. Theory 10 (2020), no. 4, pp. 1333–1359
DOI 10.4171/JST/329