---
_id: '34814'
article_type: original
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus.
    <i>Canadian Journal of Mathematics</i>. 2023;75(1):170-201. doi:<a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>
  apa: Hanusch, M. (2023). A $C^k$-seeley-extension-theorem for Bastiani’s differential
    calculus. <i>Canadian Journal of Mathematics</i>, <i>75</i>(1), 170–201. <a href="https://doi.org/10.4153/s0008414x21000596">https://doi.org/10.4153/s0008414x21000596</a>
  bibtex: '@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s
    differential calculus}, volume={75}, DOI={<a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>},
    number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical
    Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }'
  chicago: 'Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s
    Differential Calculus.” <i>Canadian Journal of Mathematics</i> 75, no. 1 (2023):
    170–201. <a href="https://doi.org/10.4153/s0008414x21000596">https://doi.org/10.4153/s0008414x21000596</a>.'
  ieee: 'M. Hanusch, “A $C^k$-seeley-extension-theorem for Bastiani’s differential
    calculus,” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, pp. 170–201,
    2023, doi: <a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>.'
  mla: Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential
    Calculus.” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, Canadian Mathematical
    Society, 2023, pp. 170–201, doi:<a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>.
  short: M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.
date_created: 2022-12-22T09:16:48Z
date_updated: 2023-02-22T11:38:32Z
department:
- _id: '93'
doi: 10.4153/s0008414x21000596
intvolume: '        75'
issue: '1'
keyword:
- extension of differentiable maps
language:
- iso: eng
page: 170-201
project:
- _id: '161'
  name: 'RegLie: Regularität von Lie-Gruppen und Lie''s Dritter Satz (RegLie)'
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
  - 1496-4279
publication_status: published
publisher: Canadian Mathematical Society
status: public
title: A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus
type: journal_article
user_id: '30905'
volume: 75
year: '2023'
...
---
_id: '40053'
author:
- first_name: P.
  full_name: Graczyk, P.
  last_name: Graczyk
- first_name: Tomasz
  full_name: Luks, Tomasz
  id: '58312'
  last_name: Luks
- first_name: P.
  full_name: Sawyer, P.
  last_name: Sawyer
citation:
  ama: Graczyk P, Luks T, Sawyer P. Potential kernels for radial Dunkl Laplacians.
    <i>Canadian Journal of Mathematics</i>. 2022;74(4):1005-1033. doi:<a href="https://doi.org/10.4153/s0008414x21000195">10.4153/s0008414x21000195</a>
  apa: Graczyk, P., Luks, T., &#38; Sawyer, P. (2022). Potential kernels for radial
    Dunkl Laplacians. <i>Canadian Journal of Mathematics</i>, <i>74</i>(4), 1005–1033.
    <a href="https://doi.org/10.4153/s0008414x21000195">https://doi.org/10.4153/s0008414x21000195</a>
  bibtex: '@article{Graczyk_Luks_Sawyer_2022, title={Potential kernels for radial
    Dunkl Laplacians}, volume={74}, DOI={<a href="https://doi.org/10.4153/s0008414x21000195">10.4153/s0008414x21000195</a>},
    number={4}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical
    Society}, author={Graczyk, P. and Luks, Tomasz and Sawyer, P.}, year={2022}, pages={1005–1033}
    }'
  chicago: 'Graczyk, P., Tomasz Luks, and P. Sawyer. “Potential Kernels for Radial
    Dunkl Laplacians.” <i>Canadian Journal of Mathematics</i> 74, no. 4 (2022): 1005–33.
    <a href="https://doi.org/10.4153/s0008414x21000195">https://doi.org/10.4153/s0008414x21000195</a>.'
  ieee: 'P. Graczyk, T. Luks, and P. Sawyer, “Potential kernels for radial Dunkl Laplacians,”
    <i>Canadian Journal of Mathematics</i>, vol. 74, no. 4, pp. 1005–1033, 2022, doi:
    <a href="https://doi.org/10.4153/s0008414x21000195">10.4153/s0008414x21000195</a>.'
  mla: Graczyk, P., et al. “Potential Kernels for Radial Dunkl Laplacians.” <i>Canadian
    Journal of Mathematics</i>, vol. 74, no. 4, Canadian Mathematical Society, 2022,
    pp. 1005–33, doi:<a href="https://doi.org/10.4153/s0008414x21000195">10.4153/s0008414x21000195</a>.
  short: P. Graczyk, T. Luks, P. Sawyer, Canadian Journal of Mathematics 74 (2022)
    1005–1033.
date_created: 2023-01-25T15:13:06Z
date_updated: 2023-01-26T17:18:50Z
department:
- _id: '555'
doi: 10.4153/s0008414x21000195
intvolume: '        74'
issue: '4'
language:
- iso: eng
page: 1005-1033
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
  - 1496-4279
publication_status: published
publisher: Canadian Mathematical Society
status: public
title: Potential kernels for radial Dunkl Laplacians
type: journal_article
user_id: '58312'
volume: 74
year: '2022'
...
---
_id: '64630'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Completeness of infinite-dimensional Lie groups in their left uniformity.
    <i>Canadian Journal of Mathematics</i>. 2019;71(1):131–152. doi:<a href="https://doi.org/10.4153/CJM-2017-048-5">10.4153/CJM-2017-048-5</a>
  apa: Glöckner, H. (2019). Completeness of infinite-dimensional Lie groups in their
    left uniformity. <i>Canadian Journal of Mathematics</i>, <i>71</i>(1), 131–152.
    <a href="https://doi.org/10.4153/CJM-2017-048-5">https://doi.org/10.4153/CJM-2017-048-5</a>
  bibtex: '@article{Glöckner_2019, title={Completeness of infinite-dimensional Lie
    groups in their left uniformity}, volume={71}, DOI={<a href="https://doi.org/10.4153/CJM-2017-048-5">10.4153/CJM-2017-048-5</a>},
    number={1}, journal={Canadian Journal of Mathematics}, author={Glöckner, Helge},
    year={2019}, pages={131–152} }'
  chicago: 'Glöckner, Helge. “Completeness of Infinite-Dimensional Lie Groups in Their
    Left Uniformity.” <i>Canadian Journal of Mathematics</i> 71, no. 1 (2019): 131–152.
    <a href="https://doi.org/10.4153/CJM-2017-048-5">https://doi.org/10.4153/CJM-2017-048-5</a>.'
  ieee: 'H. Glöckner, “Completeness of infinite-dimensional Lie groups in their left
    uniformity,” <i>Canadian Journal of Mathematics</i>, vol. 71, no. 1, pp. 131–152,
    2019, doi: <a href="https://doi.org/10.4153/CJM-2017-048-5">10.4153/CJM-2017-048-5</a>.'
  mla: Glöckner, Helge. “Completeness of Infinite-Dimensional Lie Groups in Their
    Left Uniformity.” <i>Canadian Journal of Mathematics</i>, vol. 71, no. 1, 2019,
    pp. 131–152, doi:<a href="https://doi.org/10.4153/CJM-2017-048-5">10.4153/CJM-2017-048-5</a>.
  short: H. Glöckner, Canadian Journal of Mathematics 71 (2019) 131–152.
date_created: 2026-02-26T07:03:36Z
date_updated: 2026-02-27T08:33:56Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.4153/CJM-2017-048-5
intvolume: '        71'
issue: '1'
keyword:
- '22E65'
- 22A05
- '22E67'
- 46A13
- 46M40
- 58D05
language:
- iso: eng
page: 131–152
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
quality_controlled: '1'
status: public
title: Completeness of infinite-dimensional Lie groups in their left uniformity
type: journal_article
user_id: '178'
volume: 71
year: '2019'
...
---
_id: '64667'
article_type: original
author:
- first_name: Lidia
  full_name: Birth, Lidia
  last_name: Birth
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Birth L, Glöckner H. Continuity of convolution of test functions on Lie groups.
    <i>Canadian Journal of Mathematics</i>. 2014;66(1):102–140. doi:<a href="https://doi.org/10.4153/CJM-2012-035-6">10.4153/CJM-2012-035-6</a>
  apa: Birth, L., &#38; Glöckner, H. (2014). Continuity of convolution of test functions
    on Lie groups. <i>Canadian Journal of Mathematics</i>, <i>66</i>(1), 102–140.
    <a href="https://doi.org/10.4153/CJM-2012-035-6">https://doi.org/10.4153/CJM-2012-035-6</a>
  bibtex: '@article{Birth_Glöckner_2014, title={Continuity of convolution of test
    functions on Lie groups}, volume={66}, DOI={<a href="https://doi.org/10.4153/CJM-2012-035-6">10.4153/CJM-2012-035-6</a>},
    number={1}, journal={Canadian Journal of Mathematics}, author={Birth, Lidia and
    Glöckner, Helge}, year={2014}, pages={102–140} }'
  chicago: 'Birth, Lidia, and Helge Glöckner. “Continuity of Convolution of Test Functions
    on Lie Groups.” <i>Canadian Journal of Mathematics</i> 66, no. 1 (2014): 102–140.
    <a href="https://doi.org/10.4153/CJM-2012-035-6">https://doi.org/10.4153/CJM-2012-035-6</a>.'
  ieee: 'L. Birth and H. Glöckner, “Continuity of convolution of test functions on
    Lie groups,” <i>Canadian Journal of Mathematics</i>, vol. 66, no. 1, pp. 102–140,
    2014, doi: <a href="https://doi.org/10.4153/CJM-2012-035-6">10.4153/CJM-2012-035-6</a>.'
  mla: Birth, Lidia, and Helge Glöckner. “Continuity of Convolution of Test Functions
    on Lie Groups.” <i>Canadian Journal of Mathematics</i>, vol. 66, no. 1, 2014,
    pp. 102–140, doi:<a href="https://doi.org/10.4153/CJM-2012-035-6">10.4153/CJM-2012-035-6</a>.
  short: L. Birth, H. Glöckner, Canadian Journal of Mathematics 66 (2014) 102–140.
date_created: 2026-02-26T10:57:07Z
date_updated: 2026-02-27T08:28:36Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.4153/CJM-2012-035-6
intvolume: '        66'
issue: '1'
keyword:
- '22E30'
- 46F05
- 22D15
- 42A85
- 43A10
- 43A15
- 46A03
- 46A13
- '46E25'
language:
- iso: eng
page: 102–140
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
quality_controlled: '1'
status: public
title: Continuity of convolution of test functions on Lie groups
type: journal_article
user_id: '178'
volume: 66
year: '2014'
...
---
_id: '64711'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Lie groups of measurable mappings. <i>Canadian Journal of Mathematics</i>.
    2003;55(5):969–999. doi:<a href="https://doi.org/10.4153/CJM-2003-039-9">10.4153/CJM-2003-039-9</a>
  apa: Glöckner, H. (2003). Lie groups of measurable mappings. <i>Canadian Journal
    of Mathematics</i>, <i>55</i>(5), 969–999. <a href="https://doi.org/10.4153/CJM-2003-039-9">https://doi.org/10.4153/CJM-2003-039-9</a>
  bibtex: '@article{Glöckner_2003, title={Lie groups of measurable mappings.}, volume={55},
    DOI={<a href="https://doi.org/10.4153/CJM-2003-039-9">10.4153/CJM-2003-039-9</a>},
    number={5}, journal={Canadian Journal of Mathematics}, author={Glöckner, Helge},
    year={2003}, pages={969–999} }'
  chicago: 'Glöckner, Helge. “Lie Groups of Measurable Mappings.” <i>Canadian Journal
    of Mathematics</i> 55, no. 5 (2003): 969–999. <a href="https://doi.org/10.4153/CJM-2003-039-9">https://doi.org/10.4153/CJM-2003-039-9</a>.'
  ieee: 'H. Glöckner, “Lie groups of measurable mappings.,” <i>Canadian Journal of
    Mathematics</i>, vol. 55, no. 5, pp. 969–999, 2003, doi: <a href="https://doi.org/10.4153/CJM-2003-039-9">10.4153/CJM-2003-039-9</a>.'
  mla: Glöckner, Helge. “Lie Groups of Measurable Mappings.” <i>Canadian Journal of
    Mathematics</i>, vol. 55, no. 5, 2003, pp. 969–999, doi:<a href="https://doi.org/10.4153/CJM-2003-039-9">10.4153/CJM-2003-039-9</a>.
  short: H. Glöckner, Canadian Journal of Mathematics 55 (2003) 969–999.
date_created: 2026-02-26T12:15:28Z
date_updated: 2026-02-27T07:48:12Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.4153/CJM-2003-039-9
extern: '1'
intvolume: '        55'
issue: '5'
keyword:
- '22E67'
- '46E40'
- 46T20
language:
- iso: eng
page: 969–999
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
quality_controlled: '1'
status: public
title: Lie groups of measurable mappings.
type: journal_article
user_id: '178'
volume: 55
year: '2003'
...
---
_id: '40192'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>If<jats:italic>G</jats:italic>is
    a closed subgroup of a commutative hypergroup<jats:italic>K</jats:italic>, then
    the coset space<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>carries
    a quotient hypergroup structure. In this paper, we study related convolution structures
    on<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>coming fromdeformations
    of the quotient hypergroup structure by certain functions on<jats:italic>K</jats:italic>which
    we call partial characters with respect to<jats:italic>G</jats:italic>. They are
    usually not probability-preserving, but lead to so-called signed hypergroups on<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>.
    A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted
    as a signed quotient hypergroup convolution derived from the Heisenberg group.
    Moreover, signed hypergroups associated with the Gelfand pair (<jats:italic>U</jats:italic>(<jats:italic>n</jats:italic>,
    1),<jats:italic>U</jats:italic>(<jats:italic>n</jats:italic>)) are discussed.</jats:p>
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
- first_name: Michael
  full_name: Voit, Michael
  last_name: Voit
citation:
  ama: Rösler M, Voit M. Partial Characters and Signed Quotient Hypergroups. <i>Canadian
    Journal of Mathematics</i>. 1999;51(1):96-116. doi:<a href="https://doi.org/10.4153/cjm-1999-006-6">10.4153/cjm-1999-006-6</a>
  apa: Rösler, M., &#38; Voit, M. (1999). Partial Characters and Signed Quotient Hypergroups.
    <i>Canadian Journal of Mathematics</i>, <i>51</i>(1), 96–116. <a href="https://doi.org/10.4153/cjm-1999-006-6">https://doi.org/10.4153/cjm-1999-006-6</a>
  bibtex: '@article{Rösler_Voit_1999, title={Partial Characters and Signed Quotient
    Hypergroups}, volume={51}, DOI={<a href="https://doi.org/10.4153/cjm-1999-006-6">10.4153/cjm-1999-006-6</a>},
    number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical
    Society}, author={Rösler, Margit and Voit, Michael}, year={1999}, pages={96–116}
    }'
  chicago: 'Rösler, Margit, and Michael Voit. “Partial Characters and Signed Quotient
    Hypergroups.” <i>Canadian Journal of Mathematics</i> 51, no. 1 (1999): 96–116.
    <a href="https://doi.org/10.4153/cjm-1999-006-6">https://doi.org/10.4153/cjm-1999-006-6</a>.'
  ieee: 'M. Rösler and M. Voit, “Partial Characters and Signed Quotient Hypergroups,”
    <i>Canadian Journal of Mathematics</i>, vol. 51, no. 1, pp. 96–116, 1999, doi:
    <a href="https://doi.org/10.4153/cjm-1999-006-6">10.4153/cjm-1999-006-6</a>.'
  mla: Rösler, Margit, and Michael Voit. “Partial Characters and Signed Quotient Hypergroups.”
    <i>Canadian Journal of Mathematics</i>, vol. 51, no. 1, Canadian Mathematical
    Society, 1999, pp. 96–116, doi:<a href="https://doi.org/10.4153/cjm-1999-006-6">10.4153/cjm-1999-006-6</a>.
  short: M. Rösler, M. Voit, Canadian Journal of Mathematics 51 (1999) 96–116.
date_created: 2023-01-26T08:27:14Z
date_updated: 2023-01-26T17:51:42Z
department:
- _id: '555'
doi: 10.4153/cjm-1999-006-6
extern: '1'
intvolume: '        51'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 96-116
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
  - 1496-4279
publication_status: published
publisher: Canadian Mathematical Society
status: public
title: Partial Characters and Signed Quotient Hypergroups
type: journal_article
user_id: '37390'
volume: 51
year: '1999'
...