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- W2061564877 abstract "In this article we study the abstract two parameter eigenvalue problem $$begin{gathered} T_1 u_1 = left( {lambda _1 V_{11} + lambda _2 V_{12} } right)u_1 , left| {u_1 } right| = 1 hfill T_2 u_2 = left( {lambda _1 V_{21} + lambda _2 V_{22} } right)u_2 , left| {u_2 } right| = 1 hfill end{gathered}$$ where, in the Hilbert spaces Hj, Tj is self-adjoint, bounded below and has compact resolvent, and Vjk are self-adjoint bounded operators, (−1)j+kVjk >> 0, j, k = 1, 2. An eigenvalue λ for this problem is a point in R2 satisfying both equations. Under appropriate conditions, the eigenvalues λn = (λ1 n, λ2 n) are countable and in R2. We aim to describe the set of limit points of λn/∥λn∥, as ∥λn∥ → ∞, in terms of the Vjk." @default.
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- W2061564877 date "1997-03-01" @default.
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- W2061564877 title "Two Parameter Asymptotic Spectra in the Uniformly Elliptic Case" @default.
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- W2061564877 doi "https://doi.org/10.1007/bf03322147" @default.
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