[{"article_processing_charge":"No","department":[{"_id":"JaMa"}],"date_created":"2023-01-16T09:45:31Z","publication_status":"published","intvolume":"       302","title":"Norms of certain functions of a distinguished Laplacian on the ax + b groups","scopus_import":"1","_id":"12210","issue":"4","author":[{"full_name":"Akylzhanov, Rauan","first_name":"Rauan","last_name":"Akylzhanov"},{"first_name":"Yulia","last_name":"Kuznetsova","full_name":"Kuznetsova, Yulia"},{"full_name":"Ruzhansky, Michael","first_name":"Michael","last_name":"Ruzhansky"},{"full_name":"Zhang, Haonan","first_name":"Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"publisher":"Springer Nature","article_type":"original","ec_funded":1,"quality_controlled":"1","page":"2327-2352","day":"01","arxiv":1,"doi":"10.1007/s00209-022-03143-z","abstract":[{"lang":"eng","text":"The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution kernel kt of this operator satisfies\r\n∥kt∥1≍t,∥kt∥∞≍1,\r\nso that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density of L and spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ), t>0,γ>0, and (Δ~−z)s, with complex z, s."}],"citation":{"ama":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. Norms of certain functions of a distinguished Laplacian on the ax + b groups. <i>Mathematische Zeitschrift</i>. 2022;302(4):2327-2352. doi:<a href=\"https://doi.org/10.1007/s00209-022-03143-z\">10.1007/s00209-022-03143-z</a>","apa":"Akylzhanov, R., Kuznetsova, Y., Ruzhansky, M., &#38; Zhang, H. (2022). Norms of certain functions of a distinguished Laplacian on the ax + b groups. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-022-03143-z\">https://doi.org/10.1007/s00209-022-03143-z</a>","ieee":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, and H. Zhang, “Norms of certain functions of a distinguished Laplacian on the ax + b groups,” <i>Mathematische Zeitschrift</i>, vol. 302, no. 4. Springer Nature, pp. 2327–2352, 2022.","chicago":"Akylzhanov, Rauan, Yulia Kuznetsova, Michael Ruzhansky, and Haonan Zhang. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00209-022-03143-z\">https://doi.org/10.1007/s00209-022-03143-z</a>.","short":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang, Mathematische Zeitschrift 302 (2022) 2327–2352.","mla":"Akylzhanov, Rauan, et al. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” <i>Mathematische Zeitschrift</i>, vol. 302, no. 4, Springer Nature, 2022, pp. 2327–52, doi:<a href=\"https://doi.org/10.1007/s00209-022-03143-z\">10.1007/s00209-022-03143-z</a>.","ista":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. 2022. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 302(4), 2327–2352."},"year":"2022","date_updated":"2023-08-04T09:22:14Z","external_id":{"isi":["000859680700001"],"arxiv":["2101.00584"]},"isi":1,"volume":302,"acknowledgement":"Yu. K. thanks Professor Waldemar Hebisch for valuable discussions on the general context of multipliers on Lie groups. This work was started during an ICL-CNRS fellowship of the second\r\nnamed author at the Imperial College London. Yu. K. is supported by the ANR-19-CE40-0002 grant of the French National Research Agency (ANR). H. Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. R. A. was supported by the EPSRC grant EP/R003025. M. R. is supported by the EPSRC grant EP/R003025/2 and by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations.","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"}],"oa_version":"Preprint","month":"12","publication":"Mathematische Zeitschrift","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"oa":1,"type":"journal_article","date_published":"2022-12-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.00584"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public"},{"publisher":"Springer Nature","article_type":"original","quality_controlled":"1","page":"1071–1101","file_date_updated":"2021-03-22T12:41:26Z","department":[{"_id":"TiBr"}],"date_created":"2021-03-21T23:01:21Z","article_processing_charge":"No","publication_status":"published","intvolume":"       299","title":"Arithmetic of higher-dimensional orbifolds and a mixed Waring problem","scopus_import":"1","_id":"9260","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Yamagishi","first_name":"Shuntaro","full_name":"Yamagishi, Shuntaro"}],"volume":299,"acknowledgement":"While working on this paper the authors were both supported by EPSRC grant EP/P026710/1, and the second author received additional support from the NWO Veni Grant 016.Veni.192.047. Thanks are due to Marta Pieropan, Arne Smeets and Sho Tanimoto for useful conversations related to this topic, and to the anonymous referee for numerous helpful suggestions.","ddc":["510"],"day":"05","doi":"10.1007/s00209-021-02695-w","abstract":[{"text":"We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ) when Δ is a Q-divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.","lang":"eng"}],"year":"2021","citation":{"apa":"Browning, T. D., &#38; Yamagishi, S. (2021). Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-021-02695-w\">https://doi.org/10.1007/s00209-021-02695-w</a>","ama":"Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. <i>Mathematische Zeitschrift</i>. 2021;299:1071–1101. doi:<a href=\"https://doi.org/10.1007/s00209-021-02695-w\">10.1007/s00209-021-02695-w</a>","chicago":"Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00209-021-02695-w\">https://doi.org/10.1007/s00209-021-02695-w</a>.","ieee":"T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds and a mixed Waring problem,” <i>Mathematische Zeitschrift</i>, vol. 299. Springer Nature, pp. 1071–1101, 2021.","mla":"Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” <i>Mathematische Zeitschrift</i>, vol. 299, Springer Nature, 2021, pp. 1071–1101, doi:<a href=\"https://doi.org/10.1007/s00209-021-02695-w\">10.1007/s00209-021-02695-w</a>.","short":"T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101.","ista":"Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101."},"date_updated":"2023-08-07T14:20:00Z","external_id":{"isi":["000625573800002"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","name":"Between rational and integral points","grant_number":"EP-P026710-2"}],"oa_version":"Published Version","month":"03","has_accepted_license":"1","publication":"Mathematische Zeitschrift","file":[{"success":1,"relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"9279","checksum":"8ed9f49568806894744096dbbca0ad7b","file_size":492685,"date_created":"2021-03-22T12:41:26Z","content_type":"application/pdf","file_name":"2021_MathZeitschrift_Browning.pdf","date_updated":"2021-03-22T12:41:26Z"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2021-03-05T00:00:00Z"}]