---
res:
  bibo_abstract:
  - "The aim of this paper is to find new estimates for the norms of functions of
    a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part
    is devoted to spectrally localized wave propagators, that is, functions of the
    type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution
    kernel kt of this operator satisfies\r\n∥kt∥1≍t,∥kt∥∞≍1,\r\nso that the upper
    estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary
    component, we recall the Plancherel density of L and spend certain time presenting
    and comparing different approaches to its calculation. Using its explicit form,
    we estimate uniform norms of several functions of the shifted Laplace-Beltrami
    operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ),
    t>0,γ>0, and (Δ~−z)s, with complex z, s.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Rauan
      foaf_name: Akylzhanov, Rauan
      foaf_surname: Akylzhanov
  - foaf_Person:
      foaf_givenName: Yulia
      foaf_name: Kuznetsova, Yulia
      foaf_surname: Kuznetsova
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Ruzhansky, Michael
      foaf_surname: Ruzhansky
  - foaf_Person:
      foaf_givenName: Haonan
      foaf_name: Zhang, Haonan
      foaf_surname: Zhang
      foaf_workInfoHomepage: http://www.librecat.org/personId=D8F41E38-9E66-11E9-A9E2-65C2E5697425
  bibo_doi: 10.1007/s00209-022-03143-z
  bibo_issue: '4'
  bibo_volume: 302
  dct_date: 2022^xs_gYear
  dct_identifier:
  - UT:000859680700001
  dct_isPartOf:
  - http://id.crossref.org/issn/0025-5874
  - http://id.crossref.org/issn/1432-1823
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_subject:
  - General Mathematics
  dct_title: Norms of certain functions of a distinguished Laplacian on the ax + b
    groups@
...