On the Spectrum of Some Class of Jacobi Operators in a Krein Space
A Jacobi matrix with exponential growth of its elements and a corresponding symmetric operator are considered.I t is proved that the eigenvalue problem of some self-adjoint extension of the operator in some Hilbert space is equivalent to the eigenvalue problem of a Sturm–Liouville operator with discrete self-similar weight.A n asymptotic formula for the eigenvalues distribution is obtained.T he case of an indefinite metric and self-adjoint extension of the operator in a Krein space is also considered.
KeywordsJacobi matrix self-adjoint extension of the symmetric operators eigenvalues asymptotic self-similar function Krein space
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