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dc.contributor.authorCasper, W. Riley
dc.contributor.authorGrünbaum, F. A.
dc.contributor.authorYakimov, Milen
dc.contributor.authorZurrián, Ignacio Nahuel
dc.date.accessioned2019-11-05T07:48:25Z
dc.date.available2019-11-05T07:48:25Z
dc.date.issued2019-11-05
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3680
dc.description.abstractCommuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special cases, leaving behind important families such as the operators associated to the rational solutions of the KdV equation. We prove a general theorem that the integral operator associated to every wave function in the infinite dimensional Adelic Grassmannian Gr $^{ad}$ of Wilson always reflects a differential operator (in the sense of Definition 1 below). This intrinsic property is shown to follow from the symmetries of Grassmannians of KP wave functions, where the direct commutativity property holds for operators associated to wave functions fixed by Wilson's sign involution but is violated in general. Based on this result, we prove a second main theorem that the integral operators in the computation of the singular values of the truncated generalized Laplace transforms associated to all bispectral wave functions of rank 1 reflect a differential operator. A 90$°$ rotation argument is used to prove a third main theorem that the integral operators in the computation of the singular values of the truncated generalized Fourier transforms associated to all such KP wave functions commute with a differential operator. These methods produce vast collections of integral operators with prolate-spheroidal properties, including as special cases the integral operators associated to all rational solutions of the KdV and KP hierarchies considered by Airault-McKean-Moser and Krichever, respectively, in the late 70's. Many novel examples are presented.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relationOriginally published in: Proceedings of the National Academy of Sciences, 116(2019), no. 37 pp. 18310-18315; DOI: 10.1073/pnas.1906098116. https://dx.doi.org/10.1073/pnas.1906098116en_US
dc.relation.ispartofseriesOberwolfach Preprints;2019,24
dc.titleReflective Prolate-Spheroidal Operators and the KP/KdV Equationsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2019-24
local.scientificprogramResearch in Pairs 2018en_US
local.series.idOWP-2019-24en_US
dc.identifier.urnurn:nbn:de:101:1-2019121209021849714587
local.publishers-doi10.1073/pnas.1906098116
dc.identifier.ppn1685376738


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