Abstract
The Theme of this section is the following: Suppose you find yourself on a plane domain, with only a restricted logic at your disposal; how closely can you determine which domain you are on—up to conformal equivalence? This leads to a study of a system of conformal invariants, the first-order conformal invariants (FOCI), which are obtained from the elementary properties of the algebra (or ring) of analytic functions on plane domains. Although the formal definition of FOCI is given in the terminology of mathematical logic, these invariants are nonetheless all included within the framework of classical function theory. Each of the FOCI corresponds to an elementary assertion about analytic functions that can be understood without any knowledge of mathematical logic.
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© 1984 Springer-Verlag New York Inc.
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Luecking, D.H., Rubel, L.A. (1984). First-Order Conformal Invariants. In: Complex Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8295-9_20
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DOI: https://doi.org/10.1007/978-1-4613-8295-9_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90993-6
Online ISBN: 978-1-4613-8295-9
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