• Login
    View Item 
    •   Home
    • UA Faculty Research
    • UA Faculty Publications
    • View Item
    •   Home
    • UA Faculty Research
    • UA Faculty Publications
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Inversion and Symmetries of the Star Transform

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    2005.01918.pdf
    Size:
    1.201Mb
    Format:
    PDF
    Description:
    Final Accepted Manuscript
    Download
    Author
    Ambartsoumian, Gaik
    Latifi, Mohammad J.
    Affiliation
    Department of Mathematics, University of Arizona
    Issue Date
    2021-05-03
    Keywords
    Broken ray
    Elementary symmetric polynomials
    Generalized Radon transforms
    Star transform
    V-line
    Zeros of symmetric polynomials
    
    Metadata
    Show full item record
    Publisher
    Springer Science and Business Media LLC
    Citation
    Ambartsoumian, G., Latifi, M.J. Inversion and Symmetries of the Star Transform. J Geom Anal (2021).
    Journal
    Journal of Geometric Analysis
    Rights
    © Mathematica Josephina, Inc. 2021.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    The star transform is a generalized Radon transform mapping a function of two variables to its integrals along “star-shaped” trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in mathematical models of various imaging modalities based on scattering of elementary particles. The paper presents a comprehensive study of the inversion of the star transform. We describe the necessary and sufficient conditions for invertibility of the star transform, introduce a new inversion formula and discuss its stability properties. As an unexpected bonus of our approach, we prove a conjecture from algebraic geometry about the zero sets of elementary symmetric polynomials. © 2021, Mathematica Josephina, Inc.
    Note
    12 month embargo; published: 03 May 2021
    ISSN
    1050-6926
    EISSN
    1559-002X
    DOI
    10.1007/s12220-021-00680-7
    Version
    Final accepted manuscript
    Sponsors
    National Science Foundation
    ae974a485f413a2113503eed53cd6c53
    10.1007/s12220-021-00680-7
    Scopus Count
    Collections
    UA Faculty Publications

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.