## On a trace formula of the Buslaev-Faddeev type for a long-range potential.(English)Zbl 0952.34069

The author sketches a procedure for deriving a trace formula for $$-d^2/dx^2+v(x)$$ on $$(0, +\infty[$$, with Dirichlet condition at $$0$$, where $$|v^{(n)}(x)|\leq Q (1+x)^{-\alpha-n}$$ with $$\alpha>1/2$$ and $$n=0$$, 1, 2, 3, 4. More general results and counter-examples showing the role of the various assumptions are announced. The results rely heavily on the paper by L. S. Koplienko [Sib. Math. J. 26, 365-369 (1985; Zbl 0623.47060)].

### MSC:

 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34L25 Scattering theory, inverse scattering involving ordinary differential operators 47A55 Perturbation theory of linear operators 47E05 General theory of ordinary differential operators 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

Zbl 0623.47060
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### References:

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