A conformal mapping technique for infinitely connected regions / by Maynard G. Arsove and Guy Johnson, Jr.
Methods of classical analysis devised originally for the disc are here extended to more general plane regions by the use of Green's lines, the Green's mapping, and an ideal boundary structure generalizing the prime-end structure of Carathéodory. The regions admitted include all bounded fin...
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| Online Access: |
Full Text (via ProQuest) |
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| Main Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
1970.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 91. |
| Subjects: |
MARC
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| 100 | 1 | |a Arsove, Maynard, |d 1922- | |
| 245 | 1 | 2 | |a A conformal mapping technique for infinitely connected regions / |c by Maynard G. Arsove and Guy Johnson, Jr. |
| 264 | 1 | |a Providence : |b American Mathematical Society, |c 1970. | |
| 300 | |a 1 online resource (60 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society ; |v number 91. | |
| 504 | |a Includes bibliographical references (page 56) | ||
| 505 | 0 | 0 | |t Introduction -- |t Preliminaries -- |g I. |t The Green's mapping ; |t Green's arcs -- |t The reduced region and Green's mapping -- |t Green's lines -- |t Integrals and arc length in terms of Green's coordinates -- |t Regular Green's lines -- |t Green's measure and harmonic measure -- |t Boundary properties of harmonic and analytic functions -- |g II. |t A generalized Poisson kernel and Poisson integral formula ; |t A generalization of the Poisson kernel -- |t Properties of the generalized Poisson kernel -- |t The generalized Poisson integral -- |g III. |t An invariant ideal boundary structure ; |t Construction of the boundary and its topology -- |t Further properties of the boundary -- |t Conformal invariance of the ideal boundary structure -- |t Metrizability, separability, and compactness of [script]E -- |t Termination of Green's lines in ideal boundary points -- |t The Dirichlet problem in [script]E -- |t The shaded Dirichlet problem -- |t Introduction of the hypothesis [italic]m[italic subscript]z([script]S) = |t 0. |
| 520 | |a Methods of classical analysis devised originally for the disc are here extended to more general plane regions by the use of Green's lines, the Green's mapping, and an ideal boundary structure generalizing the prime-end structure of Carathéodory. The regions admitted include all bounded finitely connected regions, as well as a broad class of infinitely connected regions. Since certain modifications in the Brelot-Choquet theory are needed to allow for singular Green's lines, an independent development of the theory of Green's lines is given, based on properties of the Green's mapping. These techniques make possible the introduction of a generalized Poisson kernel and integral defined in terms of Green's lines. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Conformal mapping. | |
| 650 | 0 | |a Poisson integral formula. | |
| 650 | 0 | |a Dirichlet problem. | |
| 650 | 0 | |a Boundary value problems. | |
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 7 | |a Poisson integral formula. |2 fast |0 (OCoLC)fst01068208. | |
| 650 | 7 | |a Mathematical analysis. |2 fast |0 (OCoLC)fst01012068. | |
| 650 | 7 | |a Dirichlet problem. |2 fast |0 (OCoLC)fst00894620. | |
| 650 | 7 | |a Boundary value problems. |2 fast |0 (OCoLC)fst00837122. | |
| 650 | 7 | |a Conformal mapping. |2 fast |0 (OCoLC)fst00875031. | |
| 700 | 1 | |a Johnson, Guy, |c Jr., |d 1922-2017, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Arsove, Maynard, 1922- |t Conformal mapping technique for infinitely connected regions. |d Providence : American Mathematical Society, 1970 |h 56 ; 26 cm |k Memoirs of the American Mathematical Society ; no. 91 |z 9780821812914. |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 91. | |
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| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |e QA360 .A77 1970eb |h Library of Congress classification |i web |n 1 |