On the number of eigenvalues in the spectral gap of a Dirac system
Don B Hinton, Angelo B. Mingarelli, Thomas T. Read, John K. Shaw · Proceedings of the Edinburgh Mathematical Society · 1986
We consider the one-dimensional operator, on 0<x<∞ with . The coefficientsp,V1andV2are assumed to be real, locally Lebesgue integrable functions;c1andc2are positive numbers. The operatorLacts in the Hilbert spaceHof all equivalence classes of complex vector-value functions such that .Lhas domainD(L)consisting of ally∈Hsuch thatyis locally absolutely continuous andLy∈H; thus in the language of differential operatorsLis a maximal operator. Associated withLis the minimal operatorL0defined as the closure of where is the restriction ofLto the functions with compact support in (0,∞).