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ASYMPTOTICS OF EIGENVALUES OF RANK-ONE PERTURBATIONS OF THE DISCRETE SCHRÖDINGER OPERATOR ON TWO-DIMENSIONAL LATTICE

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We consider the family Hvμ of discrete Schrödinger-type operator in two-dimensional lattice T2. We establish the existence or non-existence and also the finiteness of eigenvalues of Hvμ lying above the essential spectrum. Moreover, we study the properties of eigenvalues as a function of μ, in particular, we find the asymptotics of eigenvalues as sufficiently small and positive μ.

AUTHORS

F.Almuratov

Miliy unversiteti Jizzax filyali

M.Pardabaev

O'zbekiston Finlandiya pedagogika instituti

A.Bobonazarova

Milliy unversitet Jizzax filyali

Tags

# оператор# xos qiymat# собственное значение# eigenvalue# спектр# spectrum# operator# асимптотика# spektr# xos qiymat asimptotikasi# eigenvalue asymptotic

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References

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