RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2018, Volume 104, Issue 3, Pages 407–421 (Mi mz12113)  

On the Fredholm Property of a Class of Convolution-Type Operators

A. G. Kamalianab, I. M. Spitkovskyc

a Yerevan State University
b Institute of Mathematics, National Academy of Sciences of Armenia
c New York University Abu Dhabi

Abstract: The notions of the $\mathscr L$-convolution operator and the $\mathscr L$-Wiener–Hopf operator are introduced by replacing the Fourier transform in the definition of the convolution operator by a spectral transformation of the self-adjoint Sturm–Liouville operator on the axis $\mathscr L$. In the case of the zero potential, the introduced operators coincide with the convolution operator and the Wiener–Hopf integral operator, respectively. A connection between the $\mathscr L$-Wiener–Hopf operator and singular integral operators is revealed. In the case of a piecewise continuous symbol, a criterion for the Fredholm property and a formula for the index of the $\mathscr L$-Wiener–Hopf operator in terms of the symbol and the elements of the scattering matrix of the operator $\mathscr L$ are obtained.

Keywords: the operator $\mathscr L$-Wiener–Hopf, singular integral operator, Fredholm property.

Funding Agency Grant Number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia YSU-SFU-16/1
This work was supported by Science Committee, Ministry of Education and Science of Armenia, within the framework of the joint research grant no. YSU-SFU-16/1 financed according to the results of the international competition “Science Committee of Ministry of Education and Science of Armenia–Erevan State University–Southern Federal University of Russian Federation-2018.” and by Faculty Research Funding from Division of Science and Mathematics, New York University Abu Dhabi.


DOI: https://doi.org/10.4213/mzm12113

Full text: PDF file (542 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2018, 104:3, 404–416

Bibliographic databases:

UDC: 517
Received: 05.12.2017
Revised: 03.02.2018

Citation: A. G. Kamalian, I. M. Spitkovsky, “On the Fredholm Property of a Class of Convolution-Type Operators”, Mat. Zametki, 104:3 (2018), 407–421; Math. Notes, 104:3 (2018), 404–416

Citation in format AMSBIB
\Bibitem{KamSpi18}
\by A.~G.~Kamalian, I.~M.~Spitkovsky
\paper On the Fredholm Property of a Class of Convolution-Type Operators
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 3
\pages 407--421
\mathnet{http://mi.mathnet.ru/mz12113}
\crossref{https://doi.org/10.4213/mzm12113}
\elib{http://elibrary.ru/item.asp?id=35410200}
\transl
\jour Math. Notes
\yr 2018
\vol 104
\issue 3
\pages 404--416
\crossref{https://doi.org/10.1134/S0001434618090080}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000451315200008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056739330}


Linking options:
  • http://mi.mathnet.ru/eng/mz12113
  • https://doi.org/10.4213/mzm12113
  • http://mi.mathnet.ru/eng/mz/v104/i3/p407

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:164
    References:21
    First page:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020