Douglas, Jim, Jr.2016-04-222016-04-221966Buynoski, Stephanie Ruth. "A problem in harmonic continuation in a disk." (1966) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/89862">https://hdl.handle.net/1911/89862</a>.https://hdl.handle.net/1911/89862This paper treats the problem of describing the behavior of a function u bounded and harmonic in a disk, when its behavior is known on a portion B of the disk that contains an open set. If /u/ is bounded by one on the disk and bounded by E on B, then /u/ is bounded at the origin by Kie ,K2>0. The method is to complexify u, use a lemma of Carleman to bound /u/ in a neighborhood of the origin, and use a three-circle theorem of Miller to bound /u/ in the rest of the disk.17 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE0896reformatted digitalThesis Math. 1966 Buynoski