---
_id: '64569'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>We show how
    the Fourier transform for distributional sections of vector bundles over symmetric
    spaces of non‐compact type  can be used for questions of solvability of systems
    of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis–Malgrange
    theorem. We get complete solvability for the hyperbolic plane  and partial results
    for products  and the hyperbolic 3‐space .</jats:p>"
author:
- first_name: Martin
  full_name: Olbrich, Martin
  last_name: Olbrich
- first_name: Guendalina
  full_name: Palmirotta, Guendalina
  id: '109467'
  last_name: Palmirotta
citation:
  ama: Olbrich M, Palmirotta G. Solvability of invariant systems of differential equations on
    H2$\mathbb {H}^2$ and beyond. <i>Mathematische Nachrichten</i>. 2026;299(2):456-479.
    doi:<a href="https://doi.org/10.1002/mana.70100">10.1002/mana.70100</a>
  apa: Olbrich, M., &#38; Palmirotta, G. (2026). Solvability of invariant systems
    of differential equations on H2$\mathbb {H}^2$ and beyond. <i>Mathematische Nachrichten</i>,
    <i>299</i>(2), 456–479. <a href="https://doi.org/10.1002/mana.70100">https://doi.org/10.1002/mana.70100</a>
  bibtex: '@article{Olbrich_Palmirotta_2026, title={Solvability of invariant systems
    of differential equations on H2$\mathbb {H}^2$ and beyond}, volume={299}, DOI={<a
    href="https://doi.org/10.1002/mana.70100">10.1002/mana.70100</a>}, number={2},
    journal={Mathematische Nachrichten}, publisher={Wiley}, author={Olbrich, Martin
    and Palmirotta, Guendalina}, year={2026}, pages={456–479} }'
  chicago: 'Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant
    Systems of Differential Equations on H2$\mathbb {H}^2$ and Beyond.” <i>Mathematische
    Nachrichten</i> 299, no. 2 (2026): 456–79. <a href="https://doi.org/10.1002/mana.70100">https://doi.org/10.1002/mana.70100</a>.'
  ieee: 'M. Olbrich and G. Palmirotta, “Solvability of invariant systems of differential
    equations on H2$\mathbb {H}^2$ and beyond,” <i>Mathematische Nachrichten</i>,
    vol. 299, no. 2, pp. 456–479, 2026, doi: <a href="https://doi.org/10.1002/mana.70100">10.1002/mana.70100</a>.'
  mla: Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant Systems
    of Differential Equations on H2$\mathbb {H}^2$ and Beyond.” <i>Mathematische Nachrichten</i>,
    vol. 299, no. 2, Wiley, 2026, pp. 456–79, doi:<a href="https://doi.org/10.1002/mana.70100">10.1002/mana.70100</a>.
  short: M. Olbrich, G. Palmirotta, Mathematische Nachrichten 299 (2026) 456–479.
date_created: 2026-02-20T19:56:33Z
date_updated: 2026-02-20T20:01:56Z
department:
- _id: '548'
doi: 10.1002/mana.70100
intvolume: '       299'
issue: '2'
language:
- iso: eng
page: 456-479
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
  - 1522-2616
publication_status: published
publisher: Wiley
status: public
title: Solvability of invariant systems of differential equations on H2$\mathbb {H}^2$
  and beyond
type: journal_article
user_id: '109467'
volume: 299
year: '2026'
...
---
_id: '56366'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We discuss in which cases the Dunkl
    convolution  of distributions , possibly both with non‐compact support, can be
    defined and study its analytic properties. We prove results on the (singular‐)support
    of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic
    regularity for a certain class of Dunkl operators, called elliptic Dunkl operators.
    Finally, for the root system  we consider the Riesz distributions  and prove that
    their Dunkl convolution exists and that  holds.</jats:p>
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
citation:
  ama: Brennecken D. Dunkl convolution and elliptic regularity for Dunkl operators.
    <i>Mathematische Nachrichten</i>. Published online 2024. doi:<a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>
  apa: Brennecken, D. (2024). Dunkl convolution and elliptic regularity for Dunkl
    operators. <i>Mathematische Nachrichten</i>. <a href="https://doi.org/10.1002/mana.202300370">https://doi.org/10.1002/mana.202300370</a>
  bibtex: '@article{Brennecken_2024, title={Dunkl convolution and elliptic regularity
    for Dunkl operators}, DOI={<a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>},
    journal={Mathematische Nachrichten}, publisher={Wiley}, author={Brennecken, Dominik},
    year={2024} }'
  chicago: Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl
    Operators.” <i>Mathematische Nachrichten</i>, 2024. <a href="https://doi.org/10.1002/mana.202300370">https://doi.org/10.1002/mana.202300370</a>.
  ieee: 'D. Brennecken, “Dunkl convolution and elliptic regularity for Dunkl operators,”
    <i>Mathematische Nachrichten</i>, 2024, doi: <a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>.'
  mla: Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.”
    <i>Mathematische Nachrichten</i>, Wiley, 2024, doi:<a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>.
  short: D. Brennecken, Mathematische Nachrichten (2024).
date_created: 2024-10-07T11:44:00Z
date_updated: 2024-10-07T11:46:15Z
department:
- _id: '555'
doi: 10.1002/mana.202300370
language:
- iso: eng
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
  - 1522-2616
publication_status: published
publisher: Wiley
status: public
title: Dunkl convolution and elliptic regularity for Dunkl operators
type: journal_article
user_id: '55911'
year: '2024'
...
---
_id: '63260'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>A no‐flux initial‐boundary value
    problem for\r\n<jats:disp-formula/>is considered in a ball , where  and .</jats:p><jats:p>Under
    the assumption that , it is shown that for each , there exist  and a positive
    \ with the property that whenever  is nonnegative with , the global solutions
    to () emanating from the initial data  have the property that\r\n<jats:disp-formula/></jats:p>"
author:
- first_name: Yulan
  full_name: Wang, Yulan
  last_name: Wang
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Wang Y, Winkler M. A singular growth phenomenon in a Keller–Segel–type parabolic
    system involving density‐suppressed motilities. <i>Mathematische Nachrichten</i>.
    2024;297(6):2353-2364. doi:<a href="https://doi.org/10.1002/mana.202300361">10.1002/mana.202300361</a>
  apa: Wang, Y., &#38; Winkler, M. (2024). A singular growth phenomenon in a Keller–Segel–type
    parabolic system involving density‐suppressed motilities. <i>Mathematische Nachrichten</i>,
    <i>297</i>(6), 2353–2364. <a href="https://doi.org/10.1002/mana.202300361">https://doi.org/10.1002/mana.202300361</a>
  bibtex: '@article{Wang_Winkler_2024, title={A singular growth phenomenon in a Keller–Segel–type
    parabolic system involving density‐suppressed motilities}, volume={297}, DOI={<a
    href="https://doi.org/10.1002/mana.202300361">10.1002/mana.202300361</a>}, number={6},
    journal={Mathematische Nachrichten}, publisher={Wiley}, author={Wang, Yulan and
    Winkler, Michael}, year={2024}, pages={2353–2364} }'
  chicago: 'Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type
    Parabolic System Involving Density‐suppressed Motilities.” <i>Mathematische Nachrichten</i>
    297, no. 6 (2024): 2353–64. <a href="https://doi.org/10.1002/mana.202300361">https://doi.org/10.1002/mana.202300361</a>.'
  ieee: 'Y. Wang and M. Winkler, “A singular growth phenomenon in a Keller–Segel–type
    parabolic system involving density‐suppressed motilities,” <i>Mathematische Nachrichten</i>,
    vol. 297, no. 6, pp. 2353–2364, 2024, doi: <a href="https://doi.org/10.1002/mana.202300361">10.1002/mana.202300361</a>.'
  mla: Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type
    Parabolic System Involving Density‐suppressed Motilities.” <i>Mathematische Nachrichten</i>,
    vol. 297, no. 6, Wiley, 2024, pp. 2353–64, doi:<a href="https://doi.org/10.1002/mana.202300361">10.1002/mana.202300361</a>.
  short: Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364.
date_created: 2025-12-18T19:07:48Z
date_updated: 2025-12-18T20:14:46Z
doi: 10.1002/mana.202300361
intvolume: '       297'
issue: '6'
language:
- iso: eng
page: 2353-2364
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
  - 1522-2616
publication_status: published
publisher: Wiley
status: public
title: A singular growth phenomenon in a Keller–Segel–type parabolic system involving
  density‐suppressed motilities
type: journal_article
user_id: '31496'
volume: 297
year: '2024'
...
---
_id: '63309'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>This manuscript is concerned with
    the problem of efficiently estimating chemotactic gradients, as forming a ubiquitous
    issue of key importance in virtually any proof of boundedness features in Keller–Segel
    type systems. A strategy is proposed which at its core relies on bounds for such
    quantities, conditional in the sense of involving certain Lebesgue norms of solution
    components that explicitly influence the signal evolution.</jats:p><jats:p>Applications
    of this procedure firstly provide apparently novel boundedness results for two
    particular classes chemotaxis systems, and apart from that are shown to significantly
    condense proofs for basically well‐known statements on boundedness in two further
    Keller–Segel type problems.</jats:p>
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. A unifying approach toward boundedness in Keller–Segel type cross‐diffusion
    systems via conditional L∞$L^\infty$ estimates for taxis gradients. <i>Mathematische
    Nachrichten</i>. 2022;295(9):1840-1862. doi:<a href="https://doi.org/10.1002/mana.202000403">10.1002/mana.202000403</a>
  apa: Winkler, M. (2022). A unifying approach toward boundedness in Keller–Segel
    type cross‐diffusion systems via conditional L∞$L^\infty$ estimates for taxis
    gradients. <i>Mathematische Nachrichten</i>, <i>295</i>(9), 1840–1862. <a href="https://doi.org/10.1002/mana.202000403">https://doi.org/10.1002/mana.202000403</a>
  bibtex: '@article{Winkler_2022, title={A unifying approach toward boundedness in
    Keller–Segel type cross‐diffusion systems via conditional L∞$L^\infty$ estimates
    for taxis gradients}, volume={295}, DOI={<a href="https://doi.org/10.1002/mana.202000403">10.1002/mana.202000403</a>},
    number={9}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Winkler,
    Michael}, year={2022}, pages={1840–1862} }'
  chicago: 'Winkler, Michael. “A Unifying Approach toward Boundedness in Keller–Segel
    Type Cross‐diffusion Systems via Conditional L∞$L^\infty$ Estimates for Taxis
    Gradients.” <i>Mathematische Nachrichten</i> 295, no. 9 (2022): 1840–62. <a href="https://doi.org/10.1002/mana.202000403">https://doi.org/10.1002/mana.202000403</a>.'
  ieee: 'M. Winkler, “A unifying approach toward boundedness in Keller–Segel type
    cross‐diffusion systems via conditional L∞$L^\infty$ estimates for taxis gradients,”
    <i>Mathematische Nachrichten</i>, vol. 295, no. 9, pp. 1840–1862, 2022, doi: <a
    href="https://doi.org/10.1002/mana.202000403">10.1002/mana.202000403</a>.'
  mla: Winkler, Michael. “A Unifying Approach toward Boundedness in Keller–Segel Type
    Cross‐diffusion Systems via Conditional L∞$L^\infty$ Estimates for Taxis Gradients.”
    <i>Mathematische Nachrichten</i>, vol. 295, no. 9, Wiley, 2022, pp. 1840–62, doi:<a
    href="https://doi.org/10.1002/mana.202000403">10.1002/mana.202000403</a>.
  short: M. Winkler, Mathematische Nachrichten 295 (2022) 1840–1862.
date_created: 2025-12-18T19:28:46Z
date_updated: 2025-12-18T20:05:19Z
doi: 10.1002/mana.202000403
intvolume: '       295'
issue: '9'
language:
- iso: eng
page: 1840-1862
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
  - 1522-2616
publication_status: published
publisher: Wiley
status: public
title: A unifying approach toward boundedness in Keller–Segel type cross‐diffusion
  systems via conditional L∞$L^\infty$ estimates for taxis gradients
type: journal_article
user_id: '31496'
volume: 295
year: '2022'
...
---
_id: '40050'
author:
- first_name: Boris
  full_name: Baeumer, Boris
  last_name: Baeumer
- first_name: Tomasz
  full_name: Luks, Tomasz
  id: '58312'
  last_name: Luks
- first_name: Mark M.
  full_name: Meerschaert, Mark M.
  last_name: Meerschaert
citation:
  ama: Baeumer B, Luks T, Meerschaert MM. Space‐time fractional Dirichlet problems.
    <i>Mathematische Nachrichten</i>. 2018;291(17-18):2516-2535. doi:<a href="https://doi.org/10.1002/mana.201700111">10.1002/mana.201700111</a>
  apa: Baeumer, B., Luks, T., &#38; Meerschaert, M. M. (2018). Space‐time fractional
    Dirichlet problems. <i>Mathematische Nachrichten</i>, <i>291</i>(17–18), 2516–2535.
    <a href="https://doi.org/10.1002/mana.201700111">https://doi.org/10.1002/mana.201700111</a>
  bibtex: '@article{Baeumer_Luks_Meerschaert_2018, title={Space‐time fractional Dirichlet
    problems}, volume={291}, DOI={<a href="https://doi.org/10.1002/mana.201700111">10.1002/mana.201700111</a>},
    number={17–18}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Baeumer,
    Boris and Luks, Tomasz and Meerschaert, Mark M.}, year={2018}, pages={2516–2535}
    }'
  chicago: 'Baeumer, Boris, Tomasz Luks, and Mark M. Meerschaert. “Space‐time Fractional
    Dirichlet Problems.” <i>Mathematische Nachrichten</i> 291, no. 17–18 (2018): 2516–35.
    <a href="https://doi.org/10.1002/mana.201700111">https://doi.org/10.1002/mana.201700111</a>.'
  ieee: 'B. Baeumer, T. Luks, and M. M. Meerschaert, “Space‐time fractional Dirichlet
    problems,” <i>Mathematische Nachrichten</i>, vol. 291, no. 17–18, pp. 2516–2535,
    2018, doi: <a href="https://doi.org/10.1002/mana.201700111">10.1002/mana.201700111</a>.'
  mla: Baeumer, Boris, et al. “Space‐time Fractional Dirichlet Problems.” <i>Mathematische
    Nachrichten</i>, vol. 291, no. 17–18, Wiley, 2018, pp. 2516–35, doi:<a href="https://doi.org/10.1002/mana.201700111">10.1002/mana.201700111</a>.
  short: B. Baeumer, T. Luks, M.M. Meerschaert, Mathematische Nachrichten 291 (2018)
    2516–2535.
date_created: 2023-01-25T15:11:01Z
date_updated: 2023-01-26T17:19:39Z
department:
- _id: '555'
doi: 10.1002/mana.201700111
intvolume: '       291'
issue: 17-18
keyword:
- General Mathematics
language:
- iso: eng
page: 2516-2535
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
  - 1522-2616
publication_status: published
publisher: Wiley
status: public
title: Space‐time fractional Dirichlet problems
type: journal_article
user_id: '58312'
volume: 291
year: '2018'
...
---
_id: '8556'
abstract:
- lang: eng
  text: We consider the space of complete rank two collineations. Starting from its
    description as a limit of GIT-quotients of a Grassmanian G(2, n) by a certain
    $\mathbb{C}^*$-action, we determine the Cox ring by means of toric ambient modifications.
author:
- first_name: Jürgen
  full_name: Hausen, Jürgen
  last_name: Hausen
- first_name: Michael
  full_name: Liebendörfer, Michael
  id: '30933'
  last_name: Liebendörfer
  orcid: 0000-0001-9887-2074
citation:
  ama: Hausen J, Liebendörfer M. The Cox ring of the space of complete rank two collineations.
    <i>Mathematische Nachrichten</i>. 2012;285(8-9):974-980. doi:<a href="https://doi.org/10.1002/mana.201100043">10.1002/mana.201100043</a>
  apa: Hausen, J., &#38; Liebendörfer, M. (2012). The Cox ring of the space of complete
    rank two collineations. <i>Mathematische Nachrichten</i>, <i>285</i>(8–9), 974–980.
    <a href="https://doi.org/10.1002/mana.201100043">https://doi.org/10.1002/mana.201100043</a>
  bibtex: '@article{Hausen_Liebendörfer_2012, title={The Cox ring of the space of
    complete rank two collineations}, volume={285}, DOI={<a href="https://doi.org/10.1002/mana.201100043">10.1002/mana.201100043</a>},
    number={8–9}, journal={Mathematische Nachrichten}, author={Hausen, Jürgen and
    Liebendörfer, Michael}, year={2012}, pages={974–980} }'
  chicago: 'Hausen, Jürgen, and Michael Liebendörfer. “The Cox Ring of the Space of
    Complete Rank Two Collineations.” <i>Mathematische Nachrichten</i> 285, no. 8–9
    (2012): 974–80. <a href="https://doi.org/10.1002/mana.201100043">https://doi.org/10.1002/mana.201100043</a>.'
  ieee: 'J. Hausen and M. Liebendörfer, “The Cox ring of the space of complete rank
    two collineations,” <i>Mathematische Nachrichten</i>, vol. 285, no. 8–9, pp. 974–980,
    2012, doi: <a href="https://doi.org/10.1002/mana.201100043">10.1002/mana.201100043</a>.'
  mla: Hausen, Jürgen, and Michael Liebendörfer. “The Cox Ring of the Space of Complete
    Rank Two Collineations.” <i>Mathematische Nachrichten</i>, vol. 285, no. 8–9,
    2012, pp. 974–80, doi:<a href="https://doi.org/10.1002/mana.201100043">10.1002/mana.201100043</a>.
  short: J. Hausen, M. Liebendörfer, Mathematische Nachrichten 285 (2012) 974–980.
date_created: 2019-03-25T15:35:19Z
date_updated: 2026-05-13T12:08:53Z
department:
- _id: '10'
doi: 10.1002/mana.201100043
extern: '1'
intvolume: '       285'
issue: 8-9
language:
- iso: eng
page: 974-980
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 1522-2616
quality_controlled: '1'
status: public
title: The Cox ring of the space of complete rank two collineations
type: journal_article
user_id: '14972'
volume: 285
year: '2012'
...