Publication
An infinite dimensional umbral calculus
| dc.contributor.author | Finkelshtein, Dmitri L. | |
| dc.contributor.author | Kondratiev, Yuri G. | |
| dc.contributor.author | Lytvynov, Eugene | |
| dc.contributor.author | Oliveira, Maria João | |
| dc.date.accessioned | 2019-07-01T13:55:11Z | |
| dc.date.available | 2019-07-01T13:55:11Z | |
| dc.date.issued | 2019-06-16 | |
| dc.description.abstract | The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We define a sequence of monic polynomials on $\mathcal D'$, a polynomial sequence of binomial type, and a Sheffer sequence. We present equivalent conditions for a sequence of monic polynomials on $\mathcal D'$ to be of binomial type or a Sheffer sequence, respectively. We also construct a lifting of a sequence of monic polynomials on $\mathbb R$ of binomial type to a polynomial sequence of binomial type on $\mathcal D'$, and a lifting of a Sheffer sequence on $\mathbb R$ to a Sheffer sequence on $\mathcal D'$. Examples of lifted polynomial sequences include the falling and rising factorials on $\mathcal D'$, Abel, Hermite, Charlier, and Laguerre polynomials on $\mathcal D'$. Some of these polynomials have already appeared in different branches of infinite dimensional (stochastic) analysis and played there a fundamental role. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Finkelshtein, Dmitri; [et al.] - An infinite dimensional umbral calculus. "Journal of. Functional Analysis" [Em linha]. ISSN 0022-1236. Vol. 276, nº 12 (2019), p. 3714-3766 | pt_PT |
| dc.identifier.doi | 10.1016/j.jfa.2019.03.006 | pt_PT |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/8369 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Elvevier | pt_PT |
| dc.subject | Generating function | pt_PT |
| dc.subject | Polynomial sequence on D' | pt_PT |
| dc.subject | Polynomial sequence of binomial type on D' | pt_PT |
| dc.subject | Sheffer sequence on D' | pt_PT |
| dc.subject | Shift-invariance | pt_PT |
| dc.subject | Umbral calculus on D' | pt_PT |
| dc.title | An infinite dimensional umbral calculus | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 3766 | pt_PT |
| oaire.citation.issue | 12 | pt_PT |
| oaire.citation.startPage | 3714 | pt_PT |
| oaire.citation.title | Journal of Functional Analysis | pt_PT |
| oaire.citation.volume | 276 | pt_PT |
| person.familyName | Oliveira | |
| person.givenName | Maria João | |
| person.identifier.ciencia-id | DD1B-3964-2168 | |
| person.identifier.orcid | 0000-0002-4027-9849 | |
| person.identifier.scopus-author-id | 24473078000 | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | 73548978-4e91-4a20-bc3c-c62106297626 | |
| relation.isAuthorOfPublication.latestForDiscovery | 73548978-4e91-4a20-bc3c-c62106297626 |