Spectral asymptotics and trace formulas for differential operators with unbounded coefficients |
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Authors: | Kh. Kh. Murtazin V. A. Sadovnichii R. Z. Tul’kubaev |
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Affiliation: | 1. Bashkir State University, Ufa, Russia 2. Moscow State University, Moscow, Russia
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Abstract: | In the space L 2[0, π], we consider the operators $$ L = L_0 + V, L_0 = - y'' + (nu ^2 - 1/4)r^{ - 2} y (nu geqslant 1/2) $$ with the Dirichlet boundary conditions. The potential V is the operator of multiplication by a function (in general, complex-valued) in L 2[0, π] satisfying the condition $$ intlimits_0^pi {r^varepsilon } (pi - r)^varepsilon |V(r)|dr < infty , varepsilon in [0,1] $$ . We prove the trace formula Σ n=1 ∞ [µ n ? λ n ? Σ k=1 m α k (n) ] = 0. |
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