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Permutations, Signs, and Sum Ranges
dc.contributor.author | Chobanyan, Sergei | |
dc.contributor.author | Domínguez, Xabier | |
dc.contributor.author | Tarieladze, Vaja | |
dc.contributor.author | Vidal, Ricardo | |
dc.date.accessioned | 2024-02-01T16:49:57Z | |
dc.date.available | 2024-02-01T16:49:57Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Chobanyan, S.; Domínguez, X.; Tarieladze, V.; Vidal, R. Permutations, Signs, and Sum Ranges. Axioms 2023, 12, 760. https://doi.org/10.3390/axioms12080760 | es_ES |
dc.identifier.uri | http://hdl.handle.net/2183/35325 | |
dc.description.abstract | [Abstract:] The sum range SR[x; X], for a sequence x = (xn)n∈N of elements of a topological vector space X, is defined as the set of all elements s ∈ X for which there exists a bijection (=permutation) π : N → N, such that the sequence of partial sums (∑nk=1xπ(k))n∈N converges to s. The sum range problem consists of describing the structure of the sum ranges for certain classes of sequences. We present a survey of the results related to the sum range problem in finite- and infinite-dimensional cases. First, we provide the basic terminology. Next, we devote attention to the one-dimensional case, i.e., to the Riemann–Dini theorem. Then, we deal with spaces where the sum ranges are closed affine for all sequences, and we include some counterexamples. Next, we present a complete exposition of all the known results for general spaces, where the sum ranges are closed affine for sequences satisfying some additional conditions. Finally, we formulate two open questions. | es_ES |
dc.description.sponsorship | The second author was supported by the Spanish Agencia Estatal de Investigación (AEI), grant MTM2016-79422-P, cofinanced by the European Regional Development Fund (EU). | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | MDPI | es_ES |
dc.relation | info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-79422-P/ES/GRUPOS TOPOLOGICOS: DUALIDAD, GRUPOS DE LIE, APLICACIONES | es_ES |
dc.relation.uri | https://doi.org/10.3390/axioms12080760 | es_ES |
dc.rights | Atribución 3.0 España | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject | Series | es_ES |
dc.subject | Permutation | es_ES |
dc.subject | Convergence | es_ES |
dc.subject | Sum range | es_ES |
dc.title | Permutations, Signs, and Sum Ranges | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.access | info:eu-repo/semantics/openAccess | es_ES |
UDC.journalTitle | Axioms | es_ES |
UDC.volume | 12 | es_ES |
UDC.issue | 8 | es_ES |
UDC.startPage | 760 | es_ES |
dc.identifier.doi | 10.3390/axioms12080760 |
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