Computability in Harmonic Analysis

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dc.catalogadoraba
dc.contributor.authorBinder, Ilia
dc.contributor.authorGlucksam, Adi
dc.contributor.authorRojas González, Luis Cristóbal
dc.contributor.authorYampolsky, Michael
dc.date.accessioned2023-08-29T17:46:30Z
dc.date.available2023-08-29T17:46:30Z
dc.date.issued2021
dc.description.abstractWe study the question of constructive approximation of the harmonic measure omega(Omega)(x) of a bounded domain Omega with respect to a point x is an element of Omega. In particular, using a new notion of computable harmonic approximation, we show that for an arbitrary such Omega, computability of the harmonic measure omega(Omega)(x) for a single point x is an element of Omega implies computability of omega(Omega)(y) for any y is an element of Omega. This may require a different algorithm for different points y, which leads us to the construction of surprising natural examples of continuous functions that arise as solutions to a Dirichlet problem, whose values can be computed at any point, but cannot be computed with the use of the same algorithm on all of their domains. We further study the conditions under which the harmonic measure is computable uniformly, that is by a single algorithm, and characterize them for regular domains with computable boundaries.
dc.description.funderNSERC
dc.description.funderSchmidt Futures program
dc.description.funderEuropean Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant
dc.description.funderANID under the Fondecyt Regular Project
dc.fechaingreso.objetodigital2023-08-29
dc.format.extent25 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1007/s10208-021-09524-w
dc.identifier.eissn1615-3383
dc.identifier.issn1615-3375
dc.identifier.urihttps://doi.org/10.1007/s10208-021-09524-w
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/74547
dc.identifier.wosidWOS:000672106800001
dc.information.autorucInstituto de Ingeniería Matemática y Computacional; Rojas González, Luis Cristóbal; 0000-0002-9037-6102; 1182858
dc.language.isoen
dc.nota.accesoContenido completo
dc.publisherSPRINGER
dc.revistaFOUNDATIONS OF COMPUTATIONAL MATHEMATICS
dc.rightsacceso abierto
dc.subjectHarmonic measure
dc.subjectComputable analysis
dc.subjectPiece-wise computable non-computable functions
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleComputability in Harmonic Analysis
dc.typeartículo
dc.volumen22
sipa.codpersvinculados1182858
sipa.indexWoS
sipa.trazabilidadWOS;18-03-2022
sipa.trazabilidadORCID;2023-08-28
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