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Global properties of resonances for 1D Dirac operators

Evgeny Korotyaev
(Saint Petersburg State University)
Analyseseminar
Torsdag, 22 maj, 2014, at 16:15-17:15, in Aud. D3 (1531-215)
Abstrakt:
Abstract. We consider 1D Dirac operators with  compactly supported potentials. We discuss global properties of resonances. The following results are obtained:

i) the number of resonances in the complex disc with radius r is estimated in terms of the norm the potential, the diameter of its support and the radius r.

ii)  We estimate the sum of a negative power of all resonances  of the Dirac operator in terms of the norm of the
potential and the diameter of its support, i.e., we derive
Lieb-Thirring type inequalities for resonances of
the Dirac operator. The proof is based on harmonic
analysis and Carleson measures arguments. 

iii) For the Dirac operators, we determine the asymptotics of the resonance counting function at large radius.

iv)  We derive trace formulas in terms of resonances only.

This is the joint project with A. Inachenko, Sweden.
Kontaktperson: Jacob Schach Møller