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Some Remarks on Boundary Behavior of Analytic and Meromorphic Functions
| Content Provider | Scilit |
|---|---|
| Author | Bagemihl, F. Seidel, W. |
| Copyright Year | 1955 |
| Description | This paper is concerned with regular and meromorphic functions in |z| < 1 and their behavior near |z| = 1. Among the results obtained are the following. In section 2 we prove the existence of a non-constant meromorphic function that tends to zero at every point of |z| = 1 along almost all chords of |z| < 1 terminating in that point. Section 3 deals with the impossibility of ex tending this result to regular functions. In section 4 it is shown that a regular function can tend to infinity along every member of a set of spirals approach ing |z| = 1 and exhausting |z| < 1 in a simple manner. Finally, in section 5 we prove that this set of spirals cannot be replaced by an exhaustive set of Jordan arcs terminating in points of |z| = 1; Theorem 3 of this section can be interpreted as a uniqueness theorem for meromorphic functions. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/730C9678FC1A3A79263CEAEB6DCBAF3C/S0027763000023308a.pdf/div-class-title-some-remarks-on-boundary-behavior-of-analytic-and-meromorphic-functions-div.pdf |
| Ending Page | 85 |
| Page Count | 7 |
| Starting Page | 79 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000023308 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 9 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1955-10-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Meromorphic Functions |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
