2024-03-29T14:07:52Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692362022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Functions in N+ with the positive real parts on the boundaryNakazi, T.Hardy spaceexposed pointextremal problemexistence of solutionsSmirnov classouter functionpositive real part410An essentially bounded function</> on the unit circle gives a continuous linear functional T,p on the Hardy space H1 • p( </>) denotes a set of all complex numbers s such that there exists at least one function which attains the norm of T¢,-s· In a previous paper, we showed that C\p(</>) is empty or an open disc. Unfortunately we did not know when p( </>) is open or closed. In this paper, we study when p( </>) is open or closed. Moreover the functions in the Smirnov class N+ whose real parts are nonnegative on the unit circle are described and studied. Then we give new characterizations of exposed points in the unit ball of H1 and we determine when th sum of two inner functions is outer. As an result, we can describe all functions which have their Denjoy-Wolff points on the unit circle.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69236info:doi/10.14943/83632https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69236/1/pre486.pdfHokkaido University Preprint Series in Mathematics4861212000-07-01engpublisher