---
_id: '63621'
author:
- first_name: Tobias
  full_name: Black, Tobias
  id: '23686'
  last_name: Black
  orcid: 0000-0001-9963-0800
citation:
  ama: Black T. Refining Hölder regularity theory in degenerate drift-diffusion equations.
    <i>Annali di Matematica Pura ed Applicata (1923 -)</i>. Published online 2026.
    doi:<a href="https://doi.org/10.1007/s10231-025-01642-4">10.1007/s10231-025-01642-4</a>
  apa: Black, T. (2026). Refining Hölder regularity theory in degenerate drift-diffusion
    equations. <i>Annali Di Matematica Pura Ed Applicata (1923 -)</i>. <a href="https://doi.org/10.1007/s10231-025-01642-4">https://doi.org/10.1007/s10231-025-01642-4</a>
  bibtex: '@article{Black_2026, title={Refining Hölder regularity theory in degenerate
    drift-diffusion equations}, DOI={<a href="https://doi.org/10.1007/s10231-025-01642-4">10.1007/s10231-025-01642-4</a>},
    journal={Annali di Matematica Pura ed Applicata (1923 -)}, publisher={Springer
    Science and Business Media LLC}, author={Black, Tobias}, year={2026} }'
  chicago: Black, Tobias. “Refining Hölder Regularity Theory in Degenerate Drift-Diffusion
    Equations.” <i>Annali Di Matematica Pura Ed Applicata (1923 -)</i>, 2026. <a href="https://doi.org/10.1007/s10231-025-01642-4">https://doi.org/10.1007/s10231-025-01642-4</a>.
  ieee: 'T. Black, “Refining Hölder regularity theory in degenerate drift-diffusion
    equations,” <i>Annali di Matematica Pura ed Applicata (1923 -)</i>, 2026, doi:
    <a href="https://doi.org/10.1007/s10231-025-01642-4">10.1007/s10231-025-01642-4</a>.'
  mla: Black, Tobias. “Refining Hölder Regularity Theory in Degenerate Drift-Diffusion
    Equations.” <i>Annali Di Matematica Pura Ed Applicata (1923 -)</i>, Springer Science
    and Business Media LLC, 2026, doi:<a href="https://doi.org/10.1007/s10231-025-01642-4">10.1007/s10231-025-01642-4</a>.
  short: T. Black, Annali Di Matematica Pura Ed Applicata (1923 -) (2026).
date_created: 2026-01-15T10:09:43Z
date_updated: 2026-01-15T10:10:58Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s10231-025-01642-4
language:
- iso: eng
publication: Annali di Matematica Pura ed Applicata (1923 -)
publication_identifier:
  issn:
  - 0373-3114
  - 1618-1891
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Refining Hölder regularity theory in degenerate drift-diffusion equations
type: journal_article
user_id: '23686'
year: '2026'
...
---
_id: '63500'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>We prove various estimates
    for the asymptotics of counting functions associated to point sets of coherent
    frames and Riesz sequences. The obtained results recover the necessary density
    conditions for coherent frames and Riesz sequences for general unimodular amenable
    groups, while providing more precise estimates under additional localization conditions
    on the coherent system for groups of polynomial growth. \r\n</jats:p>"
author:
- first_name: Effie
  full_name: Papageorgiou, Effie
  last_name: Papageorgiou
- first_name: Jordy Timo
  full_name: van Velthoven, Jordy Timo
  last_name: van Velthoven
citation:
  ama: Papageorgiou E, van Velthoven JT. Counting function estimates for coherent
    frames and Riesz sequences. <i>Annali di Matematica Pura ed Applicata (1923 -)</i>.
    2024;204(4):1469-1491. doi:<a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>
  apa: Papageorgiou, E., &#38; van Velthoven, J. T. (2024). Counting function estimates
    for coherent frames and Riesz sequences. <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i>, <i>204</i>(4), 1469–1491. <a href="https://doi.org/10.1007/s10231-024-01535-y">https://doi.org/10.1007/s10231-024-01535-y</a>
  bibtex: '@article{Papageorgiou_van Velthoven_2024, title={Counting function estimates
    for coherent frames and Riesz sequences}, volume={204}, DOI={<a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>},
    number={4}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, publisher={Springer
    Science and Business Media LLC}, author={Papageorgiou, Effie and van Velthoven,
    Jordy Timo}, year={2024}, pages={1469–1491} }'
  chicago: 'Papageorgiou, Effie, and Jordy Timo van Velthoven. “Counting Function
    Estimates for Coherent Frames and Riesz Sequences.” <i>Annali Di Matematica Pura
    Ed Applicata (1923 -)</i> 204, no. 4 (2024): 1469–91. <a href="https://doi.org/10.1007/s10231-024-01535-y">https://doi.org/10.1007/s10231-024-01535-y</a>.'
  ieee: 'E. Papageorgiou and J. T. van Velthoven, “Counting function estimates for
    coherent frames and Riesz sequences,” <i>Annali di Matematica Pura ed Applicata
    (1923 -)</i>, vol. 204, no. 4, pp. 1469–1491, 2024, doi: <a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>.'
  mla: Papageorgiou, Effie, and Jordy Timo van Velthoven. “Counting Function Estimates
    for Coherent Frames and Riesz Sequences.” <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i>, vol. 204, no. 4, Springer Science and Business Media LLC, 2024,
    pp. 1469–91, doi:<a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>.
  short: E. Papageorgiou, J.T. van Velthoven, Annali Di Matematica Pura Ed Applicata
    (1923 -) 204 (2024) 1469–1491.
date_created: 2026-01-06T09:33:28Z
date_updated: 2026-01-06T09:38:07Z
doi: 10.1007/s10231-024-01535-y
intvolume: '       204'
issue: '4'
language:
- iso: eng
page: 1469-1491
publication: Annali di Matematica Pura ed Applicata (1923 -)
publication_identifier:
  issn:
  - 0373-3114
  - 1618-1891
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Counting function estimates for coherent frames and Riesz sequences
type: journal_article
user_id: '100325'
volume: 204
year: '2024'
...
---
_id: '63364'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. How strong singularities can be regularized by logistic degradation
    in the Keller–Segel system? <i>Annali di Matematica Pura ed Applicata (1923 -)</i>.
    2019;198(5):1615-1637. doi:<a href="https://doi.org/10.1007/s10231-019-00834-z">10.1007/s10231-019-00834-z</a>
  apa: Winkler, M. (2019). How strong singularities can be regularized by logistic
    degradation in the Keller–Segel system? <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i>, <i>198</i>(5), 1615–1637. <a href="https://doi.org/10.1007/s10231-019-00834-z">https://doi.org/10.1007/s10231-019-00834-z</a>
  bibtex: '@article{Winkler_2019, title={How strong singularities can be regularized
    by logistic degradation in the Keller–Segel system?}, volume={198}, DOI={<a href="https://doi.org/10.1007/s10231-019-00834-z">10.1007/s10231-019-00834-z</a>},
    number={5}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, publisher={Springer
    Science and Business Media LLC}, author={Winkler, Michael}, year={2019}, pages={1615–1637}
    }'
  chicago: 'Winkler, Michael. “How Strong Singularities Can Be Regularized by Logistic
    Degradation in the Keller–Segel System?” <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i> 198, no. 5 (2019): 1615–37. <a href="https://doi.org/10.1007/s10231-019-00834-z">https://doi.org/10.1007/s10231-019-00834-z</a>.'
  ieee: 'M. Winkler, “How strong singularities can be regularized by logistic degradation
    in the Keller–Segel system?,” <i>Annali di Matematica Pura ed Applicata (1923
    -)</i>, vol. 198, no. 5, pp. 1615–1637, 2019, doi: <a href="https://doi.org/10.1007/s10231-019-00834-z">10.1007/s10231-019-00834-z</a>.'
  mla: Winkler, Michael. “How Strong Singularities Can Be Regularized by Logistic
    Degradation in the Keller–Segel System?” <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i>, vol. 198, no. 5, Springer Science and Business Media LLC, 2019,
    pp. 1615–37, doi:<a href="https://doi.org/10.1007/s10231-019-00834-z">10.1007/s10231-019-00834-z</a>.
  short: M. Winkler, Annali Di Matematica Pura Ed Applicata (1923 -) 198 (2019) 1615–1637.
date_created: 2025-12-19T10:59:58Z
date_updated: 2025-12-19T11:00:04Z
doi: 10.1007/s10231-019-00834-z
intvolume: '       198'
issue: '5'
language:
- iso: eng
page: 1615-1637
publication: Annali di Matematica Pura ed Applicata (1923 -)
publication_identifier:
  issn:
  - 0373-3114
  - 1618-1891
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: How strong singularities can be regularized by logistic degradation in the
  Keller–Segel system?
type: journal_article
user_id: '31496'
volume: 198
year: '2019'
...