Approximate commutativity for a decaying potential and a function of an elliptic operator
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V. A. Sloushch
Translated by: A. V. Kiselev - St. Petersburg Math. J. 26 (2015), 849-857
- DOI: https://doi.org/10.1090/spmj/1362
- Published electronically: July 27, 2015
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Abstract:
For a continuous function $\varphi (\lambda )$, $\lambda \in \mathbb {R}$, with compact support, a bounded function $W(x)$, $x\in \mathbb {R}^{d}$, with power-like asymptotics at infinity, and a suitable selfadjoint operator $H$ in $L_{2}({\mathbb R}^{d})$, estimates for the singular values of the operator $\varphi (H)W-W\varphi (H)$ are considered. It is proved that the singular values of $\varphi (H)W-W\varphi (H)$ decay faster than those of $\varphi (H)W$. A relationship between the singular values asymptotics for the operators $\varphi (H)W$ and $\varphi ^{n}(H)W^{n}$ is also established.References
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Bibliographic Information
- V. A. Sloushch
- Affiliation: Physics Department, St. Petersburg State university, Ul′anovskaya 3, Petrodvorets, St. Petersburg 198504, Russia
- Email: vsloushch@list.ru
- Received by editor(s): March 20, 2014
- Published electronically: July 27, 2015
- Additional Notes: Supported by RFBR (grant no. 14-01-00760) and by St.Petersburg State University (grant no. 11.38.263.2014).
- © Copyright 2015 American Mathematical Society
- Journal: St. Petersburg Math. J. 26 (2015), 849-857
- MSC (2010): Primary 35P20
- DOI: https://doi.org/10.1090/spmj/1362
- MathSciNet review: 3443252