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Math. Anal."],"published-print":{"date-parts":[[2026,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We investigate the fractional dispersion of solutions to the Helmholtz equation with periodic scattering data. We show that, given appropriate rescaling, the interaction between different frequencies exhibits the same fluctuating behavior as that for the Schr\u00f6dinger equation. Since the Helmholtz equation is the stationary form of various evolution equations, this suggests that such highly fluctuating behavior is a general feature of periodic scattering on the fractional scale and not specific to the Schr\u00f6dinger setting. To achieve our result, we first establish an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.<\/jats:p>","DOI":"10.1137\/25m1769673","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T08:06:33Z","timestamp":1772611593000},"page":"868-887","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Fractional Uncertainty Principle for the Helmholtz Equation with Periodic Scattering Data"],"prefix":"10.1137","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0773-0116","authenticated-orcid":true,"given":"Javier","family":"Canto","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Basque Country UPV\/EHU, 48490 Leioa, Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nico Michele","family":"Schiavone","sequence":"additional","affiliation":[{"name":"M2ASAI, Departamento de Matem\u00e1tica e Inform\u00e1tica Aplicadas a la Ingenier\u00eda Civil y Naval, ETSI Caminos, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis","family":"Vega","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Basque Country UPV\/EHU, 48490 Leioa, Spain, and BCAM \u2013 Basque Center for Applied Mathematics, 48009 Bilbao, Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,3,4]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02786703"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/29\/20\/016"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1080\/09500349608232876"},{"key":"ref4","unstructured":"L. Boulton, G. Farmakis, B. Pelloni, and D. A. Smith, Jumps and cusps:\u00a0A new revival effect in local dispersive PDEs, https:\/\/arxiv.org\/abs\/2403.01117, 2024."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/acd489"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.109.022231"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/27\/12\/3031"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-024-03447-2"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2013.v20.n6.a7"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"R. L. 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