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  • 1. Albeverio, S
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Shelkovich, V.M.
    p-adic Colombeau-Egorov type theory of generalized functions2005In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 278, no 1-2, p. 3-16Article in journal (Refereed)
  • 2.
    Cappiello, Marco
    et al.
    University of Turin, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pseudo-differential operators in a Gelfand–Shilov setting2017In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 5-6, p. 738-755Article in journal (Refereed)
    Abstract [en]

    We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes. 

  • 3.
    Kasana, H. S.
    et al.
    Thapar Institute of Engineering and Technology, India.
    Sollervall, Håkan
    Uppsala University, Sweden.
    Approximation of unbounded functions by linear positive operators1996In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 180, no 1, p. 85-93Article in journal (Refereed)
  • 4.
    Pravda-Starov, Karel
    et al.
    Université de Rennes 1, France.
    Rodino, Luigi
    University of Turin, Italy;RUDN University, Russia.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians2018In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 1, p. 128-159Article in journal (Refereed)
    Abstract [en]

    We study propagation of the Gabor wave front set for a Schrödinger equation wit ha Hamiltonian that is the Weyl quantization of a quadratic form with nonnegativereal part. We point out that t he singular space associated with the quadratic formplays a crucial role for the understanding of this propagation. We show that the Gaborsingularities of the solution to the equation for positive times are always contained inthe singular space, and that t hey propagate in this set along the flow of the Hamiltonvector field associated with the imaginary part of the quadratic form. As an applicationwe obtain for the heat equation a sufficient condition on the Gabor wave front set of theinitial datum tempered distribution that implies regularization to Schwartz regularityfor positive times.

  • 5.
    Ruzhansky, Michael
    et al.
    Imperial College London, UK.
    Sugimoto, Mitsuru
    Nagoya University, Japan.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Tomita, Naohito
    Osaka University, Japan.
    Changes of variables in modulation and Wiener amalgam spaces2011In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 284, no 16, p. 2078-2092Article in journal (Refereed)
    Abstract [en]

    In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of such spaces and, as a consequence, we obtain several versions of local and global Beurling–Helson type theorems. We also establish a number of positive results such as local boundedness of canonical transforms on modulation spaces, properties of homogeneous changes of variables, and local continuity of Fourier integral operators on FLq. Finally, counterparts of these results are discussed for spaces on the torus.

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