dc.contributor.author | Gundersen, Gary G | |
dc.contributor.author | Heittokangas, Janne | |
dc.contributor.author | Wen, Zhi-Tao | |
dc.date.accessioned | 2020-08-18T07:41:33Z | |
dc.date.available | 2020-08-18T07:41:33Z | |
dc.date.issued | 2021 | |
dc.identifier.uri | https://erepo.uef.fi/handle/123456789/8264 | |
dc.description.abstract | Differential equations of the form f′′+A(z)f′+B(z)f=0 (*) are considered, where A(z) and B(z)≢0 are entire functions. The Lindelöf function is used to show that for any ρ∈(1/2,∞), there exists an equation of the form (*) which possesses a solution f with a Nevanlinna deficient value at 0 satisfying ρ=ρ(f)≥ρ(A)≥ρ(B), where ρ(h) denotes the order of an entire function h. It is known that such an example cannot exist when ρ≤1/2. For smaller growth functions, a geometrical modification of an example of Anderson and Clunie is used to show that for any ρ∈(2,∞), there exists an equation of the form (*) which possesses a solution f with a Valiron deficient value at 0 satisfying ρ=ρlog(f)≥ρlog(A)≥ρlog(B), where ρlog(h) denotes the logarithmic order of an entire function h. This result is essentially sharp. In both proofs, the separation of the zeros of the indicated solution plays a key role. Observations on the deficient values of solutions of linear differential equations are also given, which include a discussion of Wittich’s theorem on Nevanlinna deficient values, a modified Wittich theorem for Valiron deficient values, consequences of Gol’dberg’s theorem, and examples to illustrate possibilities that can occur. | |
dc.language.iso | englanti | |
dc.publisher | Springer Science and Business Media LLC | |
dc.relation.ispartofseries | Computational methods and function theory | |
dc.relation.uri | http://dx.doi.org/10.1007/s40315-020-00320-1 | |
dc.rights | CC BY 4.0 | |
dc.title | Deficient Values of Solutions of Linear Differential Equations | |
dc.description.version | published version | |
dc.contributor.department | Department of Physics and Mathematics, activities | |
uef.solecris.id | 71109956 | en |
dc.type.publication | Tieteelliset aikakauslehtiartikkelit | |
dc.relation.doi | 10.1007/s40315-020-00320-1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 145–177 | |
dc.publisher.country | Saksa | |
dc.relation.issn | 1617-9447 | |
dc.relation.issue | 1 | |
dc.relation.volume | 21 | |
dc.rights.accesslevel | openAccess | |
dc.type.okm | A1 | |
uef.solecris.openaccess | Hybridijulkaisukanavassa ilmestynyt avoin julkaisu | |
dc.rights.copyright | © The Authors 2020 | |
dc.type.displayType | article | en |
dc.type.displayType | artikkeli | fi |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |