Shift operators on harmonic Hilbert function spaces on real balls and von Neumann inequality

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buir.contributor.authorKaptanoğlu, H. Turgay
buir.contributor.orcidKaptanoğlu, H. Turgay|0000-0002-8795-4426
dc.citation.epage32en_US
dc.citation.issueNumber4en_US
dc.citation.spage1en_US
dc.citation.volumeNumber281en_US
dc.contributor.authorAlpay, D.
dc.contributor.authorKaptanoğlu, H. Turgay
dc.date.accessioned2022-02-21T08:42:36Z
dc.date.available2022-02-21T08:42:36Z
dc.date.issued2021-04-22
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractOn harmonic function spaces, we define shift operators using zonal harmonics and partial derivatives, and develop their basic properties. These operators turn out to be multiplications by the coordinate variables followed by projections on harmonic subspaces. This duality gives rise to a new identity for zonal harmonics. We introduce large families of reproducing kernel Hilbert spaces of harmonic functions on the unit ball of and investigate the action of the shift operators on them. We prove a dilation result for a commuting row contraction which is also what we call harmonic type. As a consequence, we show that the norm of one of our spaces is maximal among those spaces with contractive norms on harmonic polynomials. We then obtain a von Neumann inequality for harmonic polynomials of a commuting harmonic-type row contraction. This yields the maximality of the operator norm of a harmonic polynomial of the shift on making this space a natural harmonic counterpart of the Drury-Arveson space.en_US
dc.description.provenanceSubmitted by Esma Aytürk (esma.babayigit@bilkent.edu.tr) on 2022-02-21T08:42:36Z No. of bitstreams: 1 Shift_operators_on_harmonic_Hilbert_function_spaces_on_real_balls_and_von_Neumann_inequality.pdf: 531328 bytes, checksum: d5ce7f8401146ad549184d8d8a063c8d (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-21T08:42:36Z (GMT). No. of bitstreams: 1 Shift_operators_on_harmonic_Hilbert_function_spaces_on_real_balls_and_von_Neumann_inequality.pdf: 531328 bytes, checksum: d5ce7f8401146ad549184d8d8a063c8d (MD5) Previous issue date: 2021-04-22en
dc.embargo.release2023-04-22
dc.identifier.doi10.1016/j.jfa.2021.109058en_US
dc.identifier.eissn1096-0783
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/11693/77533
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://doi.org/10.1016/j.jfa.2021.109058en_US
dc.source.titleJournal of Functional Analysisen_US
dc.subjectHarmonic shiften_US
dc.subjectHarmonic type operatoren_US
dc.subjectVon Neumann inequalityen_US
dc.subjectDrury-Arveson spaceen_US
dc.titleShift operators on harmonic Hilbert function spaces on real balls and von Neumann inequalityen_US
dc.typeArticleen_US

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