Skip to main content
×
Home
    • Aa
    • Aa

The range of the Helgason-Fourier transformation on homogeneous trees

  • Michael Cowling (a1) and Alberto G. Setti (a2)
Abstract

Let be a homogeneous tree, o be a fixed reference point in , and be the closed ball of radius N in centred at o. In this paper we characterise the image under the Helgason–Fourier transformation ℋ of , the space of functions supported in , and of , the space of rapidly decreasing functions on . In both cases our results are counterparts of known results for the Helgason–Fourier transformation on noncompact symmetric spaces.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The range of the Helgason-Fourier transformation on homogeneous trees
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      The range of the Helgason-Fourier transformation on homogeneous trees
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      The range of the Helgason-Fourier transformation on homogeneous trees
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] W. Betori , J. Faraut and M. Pagliacci , ‘An inversion formula for the Radon transform on trees’, Math. Zeit. 201 (1989), 327337.

[6] S. Helgason , Geometric analysis on symmetric spaces, Math. Surveys and Monog. (Amer. Math. Soc, Providence, R.I., 1994).

[7] A. M. Mantero and A. Zappa , ‘The Poisson transform and representations of a free group’, J. Funct. Anal. 51 (1983), 372399.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax