Conditions for sectoriality and compactness of the resolvent for a non-self-adjoint Sturm--Liouville operator with singular distributional potential

2025/03/20 by Tumanov, Sergey N.
#34B05 #34L05 #34L40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2503.16172

Abstract

The aim of this paper is to find necessary and sufficient conditions for sectoriality and compactness of the resolvent for Sturm--Liouville operators with complex-valued potentials of the class q∈ W_2,loc^-1(ℝ₊) in terms of its generalized antiderivatives s∈ L_2,loc(ℝ₊).

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