[{"date_updated":"2026-02-20T20:01:56Z","publisher":"Wiley","author":[{"last_name":"Olbrich","full_name":"Olbrich, Martin","first_name":"Martin"},{"first_name":"Guendalina","last_name":"Palmirotta","id":"109467","full_name":"Palmirotta, Guendalina"}],"date_created":"2026-02-20T19:56:33Z","volume":299,"title":"Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond","doi":"10.1002/mana.70100","publication_status":"published","publication_identifier":{"issn":["0025-584X","1522-2616"]},"issue":"2","year":"2026","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>","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>.","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>","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>.","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} }","short":"M. Olbrich, G. Palmirotta, Mathematische Nachrichten 299 (2026) 456–479."},"page":"456-479","intvolume":"       299","_id":"64569","user_id":"109467","department":[{"_id":"548"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematische Nachrichten","abstract":[{"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>","lang":"eng"}],"status":"public"},{"abstract":[{"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>","lang":"eng"}],"status":"public","publication":"Mathematische Nachrichten","type":"journal_article","language":[{"iso":"eng"}],"_id":"56366","department":[{"_id":"555"}],"user_id":"55911","year":"2024","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>","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>.","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>.","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).","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} }","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>"},"publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","title":"Dunkl convolution and elliptic regularity for Dunkl operators","doi":"10.1002/mana.202300370","publisher":"Wiley","date_updated":"2024-10-07T11:46:15Z","author":[{"last_name":"Brennecken","full_name":"Brennecken, Dominik","id":"55911","first_name":"Dominik"}],"date_created":"2024-10-07T11:44:00Z"},{"date_updated":"2025-12-18T20:14:46Z","publisher":"Wiley","volume":297,"date_created":"2025-12-18T19:07:48Z","author":[{"last_name":"Wang","full_name":"Wang, Yulan","first_name":"Yulan"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"title":"A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities","doi":"10.1002/mana.202300361","publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","issue":"6","year":"2024","intvolume":"       297","page":"2353-2364","citation":{"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.","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} }","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>","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>","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>."},"_id":"63260","user_id":"31496","language":[{"iso":"eng"}],"publication":"Mathematische Nachrichten","type":"journal_article","abstract":[{"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>","lang":"eng"}],"status":"public"},{"type":"journal_article","publication":"Mathematische Nachrichten","status":"public","abstract":[{"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>","lang":"eng"}],"user_id":"31496","_id":"63309","language":[{"iso":"eng"}],"issue":"9","publication_status":"published","publication_identifier":{"issn":["0025-584X","1522-2616"]},"citation":{"short":"M. Winkler, Mathematische Nachrichten 295 (2022) 1840–1862.","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>.","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} }","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>","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>","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>.","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>."},"page":"1840-1862","intvolume":"       295","year":"2022","author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-18T19:28:46Z","volume":295,"date_updated":"2025-12-18T20:05:19Z","publisher":"Wiley","doi":"10.1002/mana.202000403","title":"A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\\infty$ estimates for taxis gradients"},{"doi":"10.1002/mana.201700111","title":"Space‐time fractional Dirichlet problems","volume":291,"date_created":"2023-01-25T15:11:01Z","author":[{"first_name":"Boris","last_name":"Baeumer","full_name":"Baeumer, Boris"},{"first_name":"Tomasz","full_name":"Luks, Tomasz","id":"58312","last_name":"Luks"},{"full_name":"Meerschaert, Mark M.","last_name":"Meerschaert","first_name":"Mark M."}],"publisher":"Wiley","date_updated":"2023-01-26T17:19:39Z","intvolume":"       291","page":"2516-2535","citation":{"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>","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>.","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} }","short":"B. Baeumer, T. Luks, M.M. Meerschaert, Mathematische Nachrichten 291 (2018) 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>.","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>"},"year":"2018","issue":"17-18","publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"department":[{"_id":"555"}],"user_id":"58312","_id":"40050","status":"public","publication":"Mathematische Nachrichten","type":"journal_article"},{"department":[{"_id":"10"}],"user_id":"30933","_id":"8556","extern":"1","language":[{"iso":"eng"}],"publication":"Mathematische Nachrichten","type":"journal_article","status":"public","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 {\\textbackslash}documentclass\\{article\\}{\\textbackslash}usepackage\\{amssymb\\}{\\textbackslash}begin\\{document\\}{\\textbackslash}pagestyle\\{empty\\}\\${\\textbackslash}mathbb \\{C\\}{\\textasciicircum}*\\${\\textbackslash}end\\{document\\}-action, we determine the Cox ring by means of toric ambient modifications."}],"volume":285,"author":[{"full_name":"Hausen, Jürgen","last_name":"Hausen","first_name":"Jürgen"},{"first_name":"Michael","last_name":"Liebendörfer","orcid":"0000-0001-9887-2074","id":"30933","full_name":"Liebendörfer, Michael"}],"date_created":"2019-03-25T15:35:19Z","date_updated":"2022-01-06T07:03:57Z","doi":"10.1002/mana.201100043","title":"The Cox ring of the space of complete rank two collineations","issue":"8-9","quality_controlled":"1","publication_identifier":{"issn":["1522-2616"]},"intvolume":"       285","page":"974-980","citation":{"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} }","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.","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>","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.","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>."},"year":"2012"}]