Show simple item record

dc.contributor.advisor MacLane, G. R.
dc.creatorRyan, Frank Beall
dc.date.accessioned 2016-04-22T21:58:40Z
dc.date.available 2016-04-22T21:58:40Z
dc.date.issued 1961
dc.identifier.citation Ryan, Frank Beall. "Regularly branched coverings and an application to Blaschke products with certain boundary characteristics." (1961) Master’s Thesis, Rice University. https://hdl.handle.net/1911/89828.
dc.identifier.urihttps://hdl.handle.net/1911/89828
dc.description.abstract The object of this thesis is two-fold: first, to treat the general existence theorems for universal (simply connected) regularly branched covering surfaces; second, to show by example how the utilization of such covering surfaces yields some interesting results in the theory of functions. In particular we shall find that there exists a Blaschke product f(z), defined in lzl < 1, which assumes as a radial limit any given value of modulus one on a set of radii having locally the power of the continuum, whose endpoints form a dense set on lzl = 1 having linear measure zero. Moreover the set of radii on which f(z) does not possess a radial limit also has locally the power of the continuum. A generalization of this example shows that, given an arbitrary perfect set E on lwl = 1, there exists a Blaschke product f(z) defined in lzl < 1 with the following properties: f(z) assumes a given value a a E as a radial limit on a set of radii having the power of the continuum, while a given value b a lwl = 1 - E is the radial limit of f(z) on a countable set of radii.
dc.format.extent 81 pp
dc.language.iso eng
dc.title Regularly branched coverings and an application to Blaschke products with certain boundary characteristics
dc.identifier.digital RICE0861
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts
dc.format.digitalOrigin reformatted digital
dc.identifier.callno Thesis Math. 1961 Ryan


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record