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Riesz basis property of Hill operators with potentials in weighted spaces

2014
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Transactions of the Moscow Mathematical Society
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Consider the Hill operator L(v) = −d 2 /dx 2 +v(x) on [0, π] with Dirichlet, periodic or antiperiodic boundary conditions; then for large enough n close to n 2 there are one Dirichlet eigenvalue μ n and two periodic (if n is even) or antiperiodic (if n is odd) eigenvalues λ − n , λ + n (counted with multiplicity). We describe classes of complex potentials v(x) = 2Z V (k)e ikx in weighted spaces (defined in terms of the Fourier coefficients of v) such that the periodic (or antiperiodic) root

doi:10.1090/s0077-1554-2014-00230-2
fatcat:7tg6v4zrzzftdbsy3ji4dkwo3m