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Open Access Green as soon as Postprint is submitted to ZB.
Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian.
Monatsh. Math. 202, 751–771 (2023)
We establish the solvability of certain linear nonhomogeneous equations and demonstrate that under reasonable technical conditions the convergence in L2(Rd) of their right sides implies the existence and the convergence in L2(Rd) of the solutions. In the first part of the work the equation involves the logarithmic Laplacian. In the second part we generalize the results derived by incorporating a shallow, short-range scalar potential into the problem. The argument relies on the methods of the spectral and scattering theory for the non-Fredholm Schrödinger type operators. As distinct from the preceding articles on the subject, for the operators involved in the equations the essential spectra fill the whole real line.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Logarithmic Laplacian ; Non-fredholm Operators ; Solvability Conditions; Integrodifferential Equations; Properness Properties; Elliptic-operators; Holder Theory; Dirichlet; Systems
ISSN (print) / ISBN
0026-9255
Journal
Monatshefte für Mathematik
Quellenangaben
Volume: 202,
Issue: 4,
Pages: 751–771
Publisher
Universität Wien
Publishing Place
Prinz-eugen-strasse 8-10, A-1040 Vienna, Austria
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)