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St. Petersburg Mathematical Journal

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Cwikel type estimates for the bordered Airy transform


Author: V. A. Sloushch
Translated by: A. V. Kiselev
Original publication: Algebra i Analiz, tom 29 (2017), nomer 2.
Journal: St. Petersburg Math. J. 29 (2018), 315-323
MSC (2010): Primary 47B10
DOI: https://doi.org/10.1090/spmj/1495
Published electronically: March 12, 2018
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Abstract: Compactness conditions as well as estimates for singular values of the bordered Airy transform $ f\mathbb{A}g$ in $ L_{2}(\mathbb{R})$ are studied for suitable functions $ f(x)$, $ g(x)$, $ x\in \mathbb{R}$. Sufficient conditions for the operator $ f\mathbb{A}g$ to be in the Schatten-von Neumann class $ \mathfrak{S}_{p}$, $ p\in (0,2)$, are obtained. In particular, certain conditions ensuring that the operator $ f\mathbb{A}g$ is in trace class are given.


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Additional Information

V. A. Sloushch
Affiliation: St. Petersburg State University, 7/9 Universitetskaya nab. 7/9, St. Petersburg 199034, Russia
Email: vsloushch@list.ru, v.slouzh@spbu.ru

DOI: https://doi.org/10.1090/spmj/1495
Keywords: Integral operators, estimates for singular values, classes of compact operators, Airy transform
Received by editor(s): November 1, 2016
Published electronically: March 12, 2018
Additional Notes: Supported by SpBSU (grant no. 11.38.263.2014) and by RFBR (grant no. 14-01-00760_a).
Dedicated: To the memory of Vladimir Savel’evich Buslaev
Article copyright: © Copyright 2018 American Mathematical Society

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