---
_id: '34829'
article_type: original
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. Differentiability of the evolution map and Mackey continuity. <i>Forum
    Mathematicum</i>. 2019;31(5):1139-1177. doi:<a href="https://doi.org/10.1515/forum-2018-0310">10.1515/forum-2018-0310</a>
  apa: Hanusch, M. (2019). Differentiability of the evolution map and Mackey continuity.
    <i>Forum Mathematicum</i>, <i>31</i>(5), 1139–1177. <a href="https://doi.org/10.1515/forum-2018-0310">https://doi.org/10.1515/forum-2018-0310</a>
  bibtex: '@article{Hanusch_2019, title={Differentiability of the evolution map and
    Mackey continuity}, volume={31}, DOI={<a href="https://doi.org/10.1515/forum-2018-0310">10.1515/forum-2018-0310</a>},
    number={5}, journal={Forum Mathematicum}, publisher={Walter de Gruyter GmbH},
    author={Hanusch, Maximilian}, year={2019}, pages={1139–1177} }'
  chicago: 'Hanusch, Maximilian. “Differentiability of the Evolution Map and Mackey
    Continuity.” <i>Forum Mathematicum</i> 31, no. 5 (2019): 1139–77. <a href="https://doi.org/10.1515/forum-2018-0310">https://doi.org/10.1515/forum-2018-0310</a>.'
  ieee: 'M. Hanusch, “Differentiability of the evolution map and Mackey continuity,”
    <i>Forum Mathematicum</i>, vol. 31, no. 5, pp. 1139–1177, 2019, doi: <a href="https://doi.org/10.1515/forum-2018-0310">10.1515/forum-2018-0310</a>.'
  mla: Hanusch, Maximilian. “Differentiability of the Evolution Map and Mackey Continuity.”
    <i>Forum Mathematicum</i>, vol. 31, no. 5, Walter de Gruyter GmbH, 2019, pp. 1139–77,
    doi:<a href="https://doi.org/10.1515/forum-2018-0310">10.1515/forum-2018-0310</a>.
  short: M. Hanusch, Forum Mathematicum 31 (2019) 1139–1177.
date_created: 2022-12-22T09:38:08Z
date_updated: 2023-01-09T18:07:13Z
department:
- _id: '93'
doi: 10.1515/forum-2018-0310
intvolume: '        31'
issue: '5'
keyword:
- regularity of Lie groups
- differentiability of the evolution map
language:
- iso: eng
page: 1139-1177
project:
- _id: '161'
  name: 'RegLie: Regularität von Lie-Gruppen und Lie''s Dritter Satz (RegLie)'
publication: Forum Mathematicum
publication_identifier:
  issn:
  - 1435-5337
  - 0933-7741
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: Differentiability of the evolution map and Mackey continuity
type: journal_article
user_id: '30905'
volume: 31
year: '2019'
...
---
_id: '64277'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Let <jats:inline-formula
    id=\"j_forum-2018-0150_ineq_9999_w2aab3b7c12b1b6b1aab1c17b1b1Aa\">\r\n                     <jats:alternatives>\r\n
    \                       <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                          <m:mrow>\r\n                              <m:mi>G</m:mi>\r\n
    \                             <m:mo>/</m:mo>\r\n                              <m:mi>H</m:mi>\r\n
    \                          </m:mrow>\r\n                        </m:math>\r\n
    \                       <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    xlink:href=\"graphic/j_forum-2018-0150_eq_0103.png\" />\r\n                        <jats:tex-math>{G/H}</jats:tex-math>\r\n
    \                    </jats:alternatives>\r\n                  </jats:inline-formula>
    be a reductive symmetric space of split rank one and let <jats:italic>K</jats:italic>
    be a maximal compact subgroup of <jats:italic>G</jats:italic>. In a previous article
    the first two authors introduced a notion of cusp forms for <jats:inline-formula
    id=\"j_forum-2018-0150_ineq_9998_w2aab3b7c12b1b6b1aab1c17b1b7Aa\">\r\n                     <jats:alternatives>\r\n
    \                       <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                          <m:mrow>\r\n                              <m:mi>G</m:mi>\r\n
    \                             <m:mo>/</m:mo>\r\n                              <m:mi>H</m:mi>\r\n
    \                          </m:mrow>\r\n                        </m:math>\r\n
    \                       <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    xlink:href=\"graphic/j_forum-2018-0150_eq_0103.png\" />\r\n                        <jats:tex-math>{G/H}</jats:tex-math>\r\n
    \                    </jats:alternatives>\r\n                  </jats:inline-formula>.
    We show that the space of cusp forms coincides with the closure of the space of
    <jats:italic>K</jats:italic>-finite generalized matrix coefficients of discrete
    series representations if and only if there exist no <jats:italic>K</jats:italic>-spherical
    discrete series representations. Moreover, we prove that every <jats:italic>K</jats:italic>-spherical
    discrete series representation occurs with multiplicity one in the Plancherel
    decomposition of <jats:inline-formula id=\"j_forum-2018-0150_ineq_9997_w2aab3b7c12b1b6b1aab1c17b1c15Aa\">\r\n
    \                    <jats:alternatives>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                          <m:mrow>\r\n                              <m:mi>G</m:mi>\r\n
    \                             <m:mo>/</m:mo>\r\n                              <m:mi>H</m:mi>\r\n
    \                          </m:mrow>\r\n                        </m:math>\r\n
    \                       <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    xlink:href=\"graphic/j_forum-2018-0150_eq_0103.png\" />\r\n                        <jats:tex-math>{G/H}</jats:tex-math>\r\n
    \                    </jats:alternatives>\r\n                  </jats:inline-formula>.</jats:p>"
author:
- first_name: Erik P.
  full_name: van den Ban, Erik P.
  last_name: van den Ban
- first_name: Job J.
  full_name: Kuit, Job J.
  last_name: Kuit
- first_name: Henrik
  full_name: Schlichtkrull, Henrik
  last_name: Schlichtkrull
citation:
  ama: van den Ban EP, Kuit JJ, Schlichtkrull H. K-invariant cusp forms for reductive
    symmetric spaces of split rank one. <i>Forum Mathematicum</i>. 2018;31(2):341-349.
    doi:<a href="https://doi.org/10.1515/forum-2018-0150">10.1515/forum-2018-0150</a>
  apa: van den Ban, E. P., Kuit, J. J., &#38; Schlichtkrull, H. (2018). K-invariant
    cusp forms for reductive symmetric spaces of split rank one. <i>Forum Mathematicum</i>,
    <i>31</i>(2), 341–349. <a href="https://doi.org/10.1515/forum-2018-0150">https://doi.org/10.1515/forum-2018-0150</a>
  bibtex: '@article{van den Ban_Kuit_Schlichtkrull_2018, title={K-invariant cusp forms
    for reductive symmetric spaces of split rank one}, volume={31}, DOI={<a href="https://doi.org/10.1515/forum-2018-0150">10.1515/forum-2018-0150</a>},
    number={2}, journal={Forum Mathematicum}, publisher={Walter de Gruyter GmbH},
    author={van den Ban, Erik P. and Kuit, Job J. and Schlichtkrull, Henrik}, year={2018},
    pages={341–349} }'
  chicago: 'Ban, Erik P. van den, Job J. Kuit, and Henrik Schlichtkrull. “K-Invariant
    Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” <i>Forum Mathematicum</i>
    31, no. 2 (2018): 341–49. <a href="https://doi.org/10.1515/forum-2018-0150">https://doi.org/10.1515/forum-2018-0150</a>.'
  ieee: 'E. P. van den Ban, J. J. Kuit, and H. Schlichtkrull, “K-invariant cusp forms
    for reductive symmetric spaces of split rank one,” <i>Forum Mathematicum</i>,
    vol. 31, no. 2, pp. 341–349, 2018, doi: <a href="https://doi.org/10.1515/forum-2018-0150">10.1515/forum-2018-0150</a>.'
  mla: van den Ban, Erik P., et al. “K-Invariant Cusp Forms for Reductive Symmetric
    Spaces of Split Rank One.” <i>Forum Mathematicum</i>, vol. 31, no. 2, Walter de
    Gruyter GmbH, 2018, pp. 341–49, doi:<a href="https://doi.org/10.1515/forum-2018-0150">10.1515/forum-2018-0150</a>.
  short: E.P. van den Ban, J.J. Kuit, H. Schlichtkrull, Forum Mathematicum 31 (2018)
    341–349.
date_created: 2026-02-19T13:28:57Z
date_updated: 2026-02-19T13:29:20Z
doi: 10.1515/forum-2018-0150
intvolume: '        31'
issue: '2'
language:
- iso: eng
page: 341-349
publication: Forum Mathematicum
publication_identifier:
  issn:
  - 1435-5337
  - 0933-7741
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: K-invariant cusp forms for reductive symmetric spaces of split rank one
type: journal_article
user_id: '52730'
volume: 31
year: '2018'
...