Spectral theory of ordinary differential operators
Spectral theory of ordinary differential operators
The spectrum of differential operators with almost constant coefficients II
Journal of Computational and Applied Mathematics - On the occasion of the 65th birthday of Prof. Michael Eastham
The spectrum of differential operators with almost constant coefficients II
Journal of Computational and Applied Mathematics - On the occasion of the 65th birthday of Prof. Michael Eastham
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The absolutely continuous spectrum of differential operators of the form Ly = w-1Σk=0n (-1)k(pky(k))(k) on L2([0, ∞),w) is determined. With pn(x),w(x) 0 the coefficients pk are assumed to satisfy pk(x) = (pkγ2kw-1)(x) → ck, γ=(w.pn-1)1/2n. If the coefficients satisfy some additional smoothness and decay conditions, the absolutely continuous part Hac of any self-adjoint extension of L is unitarily equivalent to the operator of multiplication by p(x) = Σ0n ckx2k on L2([0, ∞)). Several extensions of this result as well as examples are shown.