{"status":"public","citation":{"short":"E. Papageorgiou, Journal of Evolution Equations 24 (2024).","ama":"Papageorgiou E. Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces. <i>Journal of Evolution Equations</i>. 2024;24(2). doi:<a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>","apa":"Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces. <i>Journal of Evolution Equations</i>, <i>24</i>(2), Article 34. <a href=\"https://doi.org/10.1007/s00028-024-00959-6\">https://doi.org/10.1007/s00028-024-00959-6</a>","ieee":"E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces,” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, Art. no. 34, 2024, doi: <a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>.","bibtex":"@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}, volume={24}, DOI={<a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>}, number={234}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024} }","mla":"Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, 34, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00028-024-00959-6\">10.1007/s00028-024-00959-6</a>.","chicago":"Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal of Evolution Equations</i> 24, no. 2 (2024). <a href=\"https://doi.org/10.1007/s00028-024-00959-6\">https://doi.org/10.1007/s00028-024-00959-6</a>."},"publication_identifier":{"issn":["1424-3199","1424-3202"]},"publisher":"Springer Science and Business Media LLC","publication_status":"published","date_updated":"2024-04-17T13:20:29Z","intvolume":"        24","publication":"Journal of Evolution Equations","department":[{"_id":"555"}],"article_number":"34","issue":"2","keyword":["Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"volume":24,"year":"2024","user_id":"100325","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>This work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-<jats:italic>K</jats:italic>-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-<jats:italic>K</jats:italic>-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n                    <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without the assumption of bi-<jats:italic>K</jats:italic>-invariance.</jats:p>","lang":"eng"}],"date_created":"2024-04-17T13:18:30Z","title":"Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces","author":[{"full_name":"Papageorgiou, Efthymia","last_name":"Papageorgiou","id":"100325","first_name":"Efthymia"}],"type":"journal_article","_id":"53542","doi":"10.1007/s00028-024-00959-6"}