A discreteness criterion for the spectrum of a quasielliptic operator |
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Authors: | M G Gimadislamov |
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Institution: | 1. Bashkir State University, USSR
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Abstract: | For the spectrum of the operator $$u = \sum\nolimits_{j = 1}^n {( - 1)^{m_j } D_j^{2m_j } u + q(x)u,} $$ to be discrete, where the mj are arbitrary positive integers such that \(\sum\nolimits_{j = 1}^n {\tfrac{1}{{2m_j }}< 1} \) , and q(x) ≥ 1, it is necessary and sufficient that \(\int\limits_K {q (x) dx \to \infty } \) , when the cube K tends to infinity while preserving its dimensions. |
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