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A uniqueness theorem for a class of harmonic functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lohwater, A. J. |
| Copyright Year | 1952 |
| Abstract | where v(qf) is absolutely continuous with ,u'(q$) =v'(q$) almost everywhere, and g(q$) is of bounded variation with g'(q$) = 0 almost everywhere. Now, for any q$ for which ,u'(q$) exists, which is the case almost everywhere, lim7o1 u(r, ek) =,x'(4). Since limr,1 u(r, 0) =0 almost everywhere, we have v'(qf) =0 almost everywhere, so that v(f) in (4) is identically constant. Now, it is known2 that, for any point of discontinuity 0 of ,u(q), lim,,1 u(r, 0o) = + oo. Consequently the points |
| Starting Page | 278 |
| Ending Page | 279 |
| Page Count | 2 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1952-0046494-5 |
| Volume Number | 3 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1952-003-02/S0002-9939-1952-0046494-5/S0002-9939-1952-0046494-5.pdf |
| Alternate Webpage(s) | https://www.ams.org/journals/proc/1952-003-02/S0002-9939-1952-0046494-5/S0002-9939-1952-0046494-5.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1952-0046494-5 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
