D. R. Yafaev, “A remark concerning the theory of scattering for a perturbed polyharmonic operator”, Mat. Zametki, 15:3 (1974), 445–454; Math. Notes, 15:3 (1974), 260

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Matematicheskie Zametki, 1974, Volume 15, Issue 3, Pages 445–454 (Mi mzm7366)

This article is cited in 5 scientific papers (total in 5 papers)

A remark concerning the theory of scattering for a perturbed polyharmonic operator

D. R. Yafaev

A. A. Zhdanov Leningrad State University, USSR

Full-text PDF (750 kB) Citations (5)

Abstract: Let

$R_0$ and

$R$ be resolvents of the operators

$(-\Delta)^l$ and

$(-\Delta)^l+q$ acting in

$L_2(E^m)$ . We study the problem of the belonging of the operator

$R^P-R_0^p$ to various symmetrically-normed ideals of the ring of bounded operators. We give applications to the theory of scattering.

Received: 19.04.1973

English version:
Mathematical Notes, 1974, Volume 15, Issue 3, Pages 260–265
DOI: https://doi.org/10.1007/BF01438381

Bibliographic databases:

UDC: 517.9

Language: Russian

Citation: D. R. Yafaev, “A remark concerning the theory of scattering for a perturbed polyharmonic operator”, Mat. Zametki, 15:3 (1974), 445–454; Math. Notes, 15:3 (1974), 260–265

Citation in format AMSBIB

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\by D.~R.~Yafaev

\paper A~remark concerning the theory of scattering for a~perturbed polyharmonic operator

\jour Mat. Zametki

\yr 1974

\vol 15

\issue 3

\pages 445--454

\mathnet{http://mi.mathnet.ru/mzm7366}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=348298}

\zmath{https://zbmath.org/?q=an:0309.47010|0302.47007}

\transl

\jour Math. Notes

\yr 1974

\vol 15

\issue 3

\pages 260--265

\crossref{https://doi.org/10.1007/BF01438381}

Linking options:

https://www.mathnet.ru/eng/mzm7366

https://www.mathnet.ru/eng/mzm/v15/i3/p445

This publication is cited in the following 5 articles:

Rupert L. Frank, Alexander Pushnitski, “Schatten Class Conditions for Functions of Schrödinger Operators”, Ann. Henri Poincaré, 20:11 (2019), 3543
Rupert L. Frank, Alexander Pushnitski, “Trace Class Conditions for Functions of Schrödinger Operators”, Commun. Math. Phys., 335:1 (2015), 477
D. R. Yafaev, “The Schrödinger Operator: Perturbation Determinants, the Spectral Shift Function, Trace Identities, and All That”, Funct. Anal. Appl., 41:3 (2007), 217–236
V. F. Kovalenko, Yu. A. Semenov, “Some problems on expansion in generalized eigenfunctions of the Schrödinger operator with strongly singular potentials”, Russian Math. Surveys, 33:4 (1978), 119–157
J. Avron, I. Herbst, B. Simon, “Schrödinger operators with magnetic fields. I. general interactions”, Duke Math. J., 45:4 (1978)

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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