[{"scopus_import":"1","doi":"10.2140/paa.2025.7.1","OA_place":"repository","status":"public","type":"journal_article","date_published":"2025-01-22T00:00:00Z","intvolume":"         7","oa_version":"Preprint","language":[{"iso":"eng"}],"keyword":["dispersive equations","nonlinear wave equation","semilinear wave equation","scattering","inverse scattering","deconvolution"],"volume":7,"external_id":{"arxiv":["2307.00829"]},"month":"01","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2307.00829","open_access":"1"}],"quality_controlled":"1","OA_type":"green","day":"22","article_processing_charge":"No","publication_status":"published","extern":"1","mathsc":["35L70","35P25","35R30"],"arxiv":1,"date_updated":"2026-06-24T13:24:38Z","publication":"Pure and Applied Analysis","title":"Deconvolutional determination of the nonlinearity in a semilinear wave equation","author":[{"first_name":"Nicholas","last_name":"Hu","full_name":"Hu, Nicholas"},{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica"}],"page":"1-17","abstract":[{"text":"We demonstrate that in three space dimensions, the scattering behaviour of semilinear wave equations with quintic-type nonlinearities uniquely determines the nonlinearity. The nonlinearity is permitted to depend on both space and time.","lang":"eng"}],"year":"2025","_id":"22027","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"oa":1,"citation":{"chicago":"Hu, Nicholas, Rowan Killip, and Monica Vişan. “Deconvolutional Determination of the Nonlinearity in a Semilinear Wave Equation.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/paa.2025.7.1\">https://doi.org/10.2140/paa.2025.7.1</a>.","short":"N. Hu, R. Killip, M. Vişan, Pure and Applied Analysis 7 (2025) 1–17.","ista":"Hu N, Killip R, Vişan M. 2025. Deconvolutional determination of the nonlinearity in a semilinear wave equation. Pure and Applied Analysis. 7(1), 1–17.","ama":"Hu N, Killip R, Vişan M. Deconvolutional determination of the nonlinearity in a semilinear wave equation. <i>Pure and Applied Analysis</i>. 2025;7(1):1-17. doi:<a href=\"https://doi.org/10.2140/paa.2025.7.1\">10.2140/paa.2025.7.1</a>","mla":"Hu, Nicholas, et al. “Deconvolutional Determination of the Nonlinearity in a Semilinear Wave Equation.” <i>Pure and Applied Analysis</i>, vol. 7, no. 1, Mathematical Sciences Publishers, 2025, pp. 1–17, doi:<a href=\"https://doi.org/10.2140/paa.2025.7.1\">10.2140/paa.2025.7.1</a>.","apa":"Hu, N., Killip, R., &#38; Vişan, M. (2025). Deconvolutional determination of the nonlinearity in a semilinear wave equation. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2025.7.1\">https://doi.org/10.2140/paa.2025.7.1</a>","ieee":"N. Hu, R. Killip, and M. Vişan, “Deconvolutional determination of the nonlinearity in a semilinear wave equation,” <i>Pure and Applied Analysis</i>, vol. 7, no. 1. Mathematical Sciences Publishers, pp. 1–17, 2025."},"article_type":"original","issue":"1","date_created":"2026-06-19T07:36:00Z","publisher":"Mathematical Sciences Publishers","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.2140/paa.2025.7.1"},{"OA_type":"green","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1503.02716","open_access":"1"}],"month":"04","volume":288,"external_id":{"arxiv":["1503.02716"]},"language":[{"iso":"eng"}],"oa_version":"Preprint","intvolume":"       288","type":"journal_article","date_published":"2018-04-01T00:00:00Z","status":"public","OA_place":"repository","doi":"10.1007/s00209-017-1934-8","scopus_import":"1","fulldoi":"https://doi.org/10.1007/s00209-017-1934-8","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","date_created":"2026-06-19T07:46:14Z","issue":"3-4","article_type":"original","citation":{"short":"R. Killip, C. Miao, M. Vişan, J. Zhang, J. Zheng, Mathematische Zeitschrift 288 (2018) 1273–1298.","chicago":"Killip, R., C. Miao, Monica Vişan, J. Zhang, and J. Zheng. “Sobolev Spaces Adapted to the Schrödinger Operator with Inverse-Square Potential.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00209-017-1934-8\">https://doi.org/10.1007/s00209-017-1934-8</a>.","ieee":"R. Killip, C. Miao, M. Vişan, J. Zhang, and J. Zheng, “Sobolev spaces adapted to the Schrödinger operator with inverse-square potential,” <i>Mathematische Zeitschrift</i>, vol. 288, no. 3–4. Springer Nature, pp. 1273–1298, 2018.","mla":"Killip, R., et al. “Sobolev Spaces Adapted to the Schrödinger Operator with Inverse-Square Potential.” <i>Mathematische Zeitschrift</i>, vol. 288, no. 3–4, Springer Nature, 2018, pp. 1273–98, doi:<a href=\"https://doi.org/10.1007/s00209-017-1934-8\">10.1007/s00209-017-1934-8</a>.","ama":"Killip R, Miao C, Vişan M, Zhang J, Zheng J. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. <i>Mathematische Zeitschrift</i>. 2018;288(3-4):1273-1298. doi:<a href=\"https://doi.org/10.1007/s00209-017-1934-8\">10.1007/s00209-017-1934-8</a>","apa":"Killip, R., Miao, C., Vişan, M., Zhang, J., &#38; Zheng, J. (2018). Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-017-1934-8\">https://doi.org/10.1007/s00209-017-1934-8</a>","ista":"Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2018. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift. 288(3–4), 1273–1298."},"oa":1,"publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"year":"2018","_id":"22042","abstract":[{"lang":"eng","text":"We study the L p-theory for the Schrödinger operatorLa with inverse-square potential\r\na|x|^−2. Our main result describes when L p-based Sobolev spaces defined in terms of the\r\noperator (La)^s/2 agree with those defined via (−\u0002)^s/2.We consider all regularities 0 < s < 2.\r\nIn order to make the paper self-contained, we also review (with proofs) multiplier theorems,\r\nLittlewood–Paley theory, and Hardy-type inequalities associated to the operator La."}],"page":"1273-1298","author":[{"last_name":"Killip","full_name":"Killip, R.","first_name":"R."},{"first_name":"C.","last_name":"Miao","full_name":"Miao, C."},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica"},{"full_name":"Zhang, J.","last_name":"Zhang","first_name":"J."},{"full_name":"Zheng, J.","last_name":"Zheng","first_name":"J."}],"title":"Sobolev spaces adapted to the Schrödinger operator with inverse-square potential","publication":"Mathematische Zeitschrift","arxiv":1,"date_updated":"2026-06-25T07:36:26Z","mathsc":["35P25","35Q55"],"extern":"1","publication_status":"published","day":"01","article_processing_charge":"No"}]