Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Phragmén-Lindelöf theorem in a cohomological form
HTML articles powered by AMS MathViewer

by Ching Her Lin PDF
Proc. Amer. Math. Soc. 89 (1983), 589-597 Request permission

Abstract:

The main result of this paper is as follows. Given functons ${\phi _1}(\varepsilon ), \ldots ,{\phi _\nu }(\varepsilon )$ which are holomorphic in sectors ${S_1}, \ldots ,{S_p}$, respectively, where ${S_1} \cup \cdots \cup {S_\nu } = \{ \varepsilon :|\arg \varepsilon | < \pi /2\alpha ,0|\varepsilon | < \rho \}$ for $\alpha > 1$, $\rho > 0$, set ${\phi _{jk}} = {\phi _j} - {\phi _k}$ if ${S_j} \cap {S_k} \ne \emptyset$. Then $\{ {\phi _{jk}}\}$ satisfy cocycle conditions ${\phi _{jk}} + {\phi _{kl}} = {\phi _{jl}}$ whenever ${S_j} \cap {S_k} \cap {S_l} \ne \emptyset$. In addition to the conditions $|{\phi _1}| < {M_0}$ and $|{\phi _\nu }| < {M_0}$ on the two rays of the boundary $({\text {i}}{\text {.e}}{\text {. }}\arg \varepsilon = \pi /2\alpha )$, and $|{\phi _j}(\varepsilon )| \leqslant A\exp (c/|\varepsilon |)$ in ${S_j}$ for some positive numbers $A$ and $c$, $j = 1,2, \ldots ,\nu$, if the $\{ {\phi _j}\}$ satisfy the conditions $\{ {\phi _{jk}}\} < {M_0}$ on ${S_j} \cap {S_k}( \ne \emptyset )$, then we get $|{\phi _j}| < M$ on $S$, $j = 1,2, \ldots ,\nu$. (From the cohomological point of view, we can get global results for ${\phi _j}$,oce the local data on cocycles is known.)
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A10
  • Retrieve articles in all journals with MSC: 30A10
Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 589-597
  • MSC: Primary 30A10
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718979-7
  • MathSciNet review: 718979