Two problems in function theory of one complex variable: local properties of solutions of second-order differential equations and number of deficient functions of some entire functions

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dc.contributor.authorCheng, Jiuyien
dc.contributor.committeechairRossi, John F.en
dc.contributor.committeememberMurray, M. M.en
dc.contributor.committeememberOlin, Robert F.en
dc.contributor.committeememberSnider, Robert L.en
dc.contributor.committeememberWheeler, Robert L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:14:51Zen
dc.date.adate2006-06-07en
dc.date.available2014-03-14T21:14:51Zen
dc.date.issued1994-01-04en
dc.date.rdate2006-06-07en
dc.date.sdate2006-06-07en
dc.description.abstractThis dissertation investigates two problems in the function theory of one complex variable. In Chapter 1, we study the asymptotics and zero distribution of solutions of the differential equation w<sup>n</sup> + A(z)w = 0, where A(z) is a transcendental entire function of very slow growth. The result parallels the classical case when A(z) is assumed to be a polynomial. An analogue concerning the case when A(z) is a transcendental entire function whose series expansion satisfies the Hadamard gap condition is given. In Chapter 2, we give upper bounds for the number of deficient functions of entire functions of completely regular growth and entire functions whose zeros have angular densities. In particular, the bound is 2λ + 1 if the entire function is of completely regular growth with order λ, 0 < λ < ∞.en
dc.description.degreePh. D.en
dc.format.extentvi, 62 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06072006-124203en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06072006-124203/en
dc.identifier.urihttp://hdl.handle.net/10919/38553en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1994.C546.pdfen
dc.relation.isformatofOCLC# 30760495en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1994.C546en
dc.subject.lcshDifferential equations -- Numerical solutionsen
dc.subject.lcshFunctions, Entireen
dc.titleTwo problems in function theory of one complex variable: local properties of solutions of second-order differential equations and number of deficient functions of some entire functionsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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