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dc.contributor.authorGundersen, Gary G
dc.contributor.authorHeittokangas, Janne
dc.contributor.authorWen, Zhi-Tao
dc.date.accessioned2020-08-18T07:41:33Z
dc.date.available2020-08-18T07:41:33Z
dc.date.issued2020
dc.identifier.urihttps://erepo.uef.fi/handle/123456789/8264
dc.description.abstractDifferential 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.isoenglanti
dc.publisherSpringer Science and Business Media LLC
dc.relation.ispartofseriesComputational methods and function theory
dc.relation.urihttp://dx.doi.org/10.1007/s40315-020-00320-1
dc.rightsCC BY http://creativecommons.org/licenses/by/4.0/
dc.titleDeficient Values of Solutions of Linear Differential Equations
dc.description.versionpublished version
dc.contributor.departmentDepartment of Physics and Mathematics, activities
uef.solecris.id71109956en
dc.type.publicationTieteelliset aikakauslehtiartikkelit
dc.rights.accessrights© The Authors 2020
dc.relation.doi10.1007/s40315-020-00320-1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange145–177
dc.publisher.countrySaksa
dc.relation.issn1617-9447
dc.relation.issue1
dc.relation.volume21
dc.rights.accesslevelopenAccess
dc.type.okmA1
uef.solecris.openaccessHybridijulkaisukanavassa ilmestynyt avoin julkaisu


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