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Higher-order trace formulas for contractive and dissipative operators
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 15 August 2025, pp. 1-26
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We establish higher-order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator of the contractions and significantly enlarging the set of admissible functions. We also derive higher-order trace formulas for maximal dissipative operators under relaxed assumptions and new simplified trace formulas for unitary and resolvent comparable self-adjoint operators. The respective spectral shift measures are absolutely continuous and, in the case of contractions, the set of admissible functions for the nth-order trace formula on the unit circle includes the Besov class
$B^n_{\infty , 1}(\mathbb {T})$. Both aforementioned properties are new in the mentioned generality.
Semi-classical Asymptotics for the Schrödinger Operator with Oscillating Decaying Potential
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 4 / 01 December 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 734-747
- Print publication:
- 01 December 2016
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We study the distribution of the discrete spectrumof the Schrödinger operator perturbed by a fast oscillating decaying potential depending on a small parameter
$h$ .
