Asymptotics of eigenvalues for a class of singular Kreĭn strings
نویسنده
چکیده
AKreı̆n string is (essentially) a pairS[L ,m]where 0 < L ≤ ∞ andm : [0, L) → [0,∞) is nondecreasing. Each string gives rise to an operator model, the Kreı̆n-Feller differential operator−DmDx acting in the space L2(dm). This operator has a selfadjoint realization which is nonnegative. Provided that L + limx→L m(x) < ∞, this realization has discrete spectrum and, when (λn) denotes the sequence of positive eigenvalues arranged increasingly, then lim n √ λn = 1 π L ∫
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