Publication
Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis
| dc.contributor.author | Finkelshtein, Dmitri L. | |
| dc.contributor.author | Kondratiev, Yuri G. | |
| dc.contributor.author | Lytvynov, Eugene | |
| dc.contributor.author | Oliveira, Maria João | |
| dc.contributor.author | Streit, Ludwig | |
| dc.date.accessioned | 2019-09-30T11:10:35Z | |
| dc.date.available | 2019-09-30T11:10:35Z | |
| dc.date.issued | 2019-11-01 | |
| dc.description.abstract | For certain Sheffer sequences $(s_n)_{n=0}^\infty$ on $\mathbb C$, Grabiner (1988) proved that, for each $\alpha\in[0,1]$, the corresponding Sheffer operator $z^n\mapsto s_n(z)$ extends to a linear self-homeomorphism of $\mathcal E^{\alpha}_{\mathrm{min}}(\mathbb C)$, the Fréchet topological space of entire functions of exponential order $\alpha$ and minimal type. In particular, every function $f\in \mathcal E^{\alpha}_{\mathrm{min}}(\mathbb C)$ admits a unique decomposition $f(z)=\sum_{n=0}^\infty c_n s_n(z)$, and the series converges in the topology of $\mathcal E^{\alpha}_{\mathrm{min}}(\mathbb C)$. Within the context of a complex nuclear space $\Phi$ and its dual space $\Phi'$, in this work we generalize Grabiner's result to the case of Sheffer operators corresponding to Sheffer sequences on $\Phi'$. In particular, for $\Phi=\Phi'=\mathbb C^n$ with $n\ge2$, we obtain the multivariate extension of Grabiner's theorem. Furthermore, for an Appell sequence on a general co-nuclear space $\Phi'$, we find a sufficient condition for the corresponding Sheffer operator to extend to a linear self-homeomorphism of $\mathcal E^{\alpha}_{\mathrm{min}}(\Phi')$ when $\alpha>1$. The latter result is new even in the one-dimensional case. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Finkelshtein, Dmitri [et al.] - Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis. "Journal of Mathematical Analysis and Applications" [Em linha]. ISSN 0022-247X. Vol. 479, nº 1 (2019), p. 162-184 | pt_PT |
| dc.identifier.doi | 10.1016/j.jmaa.2019.06.021 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/8550 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Elsevier | pt_PT |
| dc.subject | Infinite dimensional holomorphy | pt_PT |
| dc.subject | Nuclear and co-nuclear spaces | pt_PT |
| dc.subject | Polynomials sequence of binomial type | pt_PT |
| dc.subject | Sheffer operator | pt_PT |
| dc.subject | Sheffer sequence | pt_PT |
| dc.subject | Spaces of entire functions | pt_PT |
| dc.title | Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 184 | pt_PT |
| oaire.citation.startPage | 162 | pt_PT |
| oaire.citation.title | Journal of Mathematical Analysis and Applications | 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 |