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2 results

  • WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS

  • Part of
  • TAPENDU RANA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 116 / Issue 1 / February 2024
    Published online by Cambridge University Press:
    18 July 2023, pp. 68-95
    Print publication:
    February 2024
    • Article
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  • We prove Wiener Tauberian theorem type results for various spaces of radial functions, which are Banach algebras on a real-rank-one semisimple Lie group G. These are natural generalizations of the Wiener Tauberian theorem for the commutative Banach algebra of the integrable radial functions on G.

  • 2 - Global Attraction to Solitons

  • Alexander Komech, Universität Wien, Austria, Elena Kopylova, Universität Wien, Austria
  • Book:
    Attractors of Hamiltonian Nonlinear Partial Differential Equations
    Published online:
    17 September 2021
    Print publication:
    30 September 2021, pp 77-90

  • Summary

    In this chapterwe present thefirst results on global attraction tosolitons forthe scalar wave field and the Maxwell field coupled to the charged relativistic particlewith density of charge satisfying the Wiener condition. In particular, the radiation damping in classical electrodynamics is rigorously proved for the first time (in this chapter, for the translation-invariant case). The proofs rely on calculation of energy radiation to infinity and canonical transformation to the comoving frame and use energy bound from below and the Wiener Tauberian theorem.