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Mat. Zametki, 2015, Volume 97, Issue 4, Pages 493–502 (Mi mz10523)  

This article is cited in 1 scientific paper (total in 1 paper)

Reduction of Nonlocal Pseudodifferential Operators on a Noncompact Manifold to Classical Pseudodifferential Operators on a Double-Dimensional Compact Manifold

A. A. Arutyunov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: In the present paper, we obtain some Fredholmness criteria and a formula for the index of nonlocal pseudodifferential operators generated by shifts and multiplications by periodic functions and acting in the Schwartz space $\mathcal{S}(\mathbb{R}^n)$. These results significantly differ from the results known to the author in this field of study, namely, the Fredholmness criteria and the formula for the index of nonlocal pseudodifferential operators acting over the noncompact manifold $\mathbb{R}^n$ are obtained here for the first time.

Keywords: nonlocal pseudodifferential operator, Fredholmness criterion, index of elliptic pseudodifferential operators, Schwartz space.

DOI: https://doi.org/10.4213/mzm10523

Full text: PDF file (504 kB)
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English version:
Mathematical Notes, 2015, 97:4, 502–509

Bibliographic databases:

UDC: 515.168.5+517.983.37
Received: 17.02.2014

Citation: A. A. Arutyunov, “Reduction of Nonlocal Pseudodifferential Operators on a Noncompact Manifold to Classical Pseudodifferential Operators on a Double-Dimensional Compact Manifold”, Mat. Zametki, 97:4 (2015), 493–502; Math. Notes, 97:4 (2015), 502–509

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v97/i4/p493

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. B. Bazarkhanov, “($L_p$$L_q$)-Boundedness of Pseudodifferential Operators on the $n$-Dimensional Torus”, Math. Notes, 102:6 (2017), 873–877  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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