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Unicity of Meromorphic Mappings: Advances in Complex Analysis and Its Applications, cartea 1

Autor Pei-Chu Hu, Ping Li, Chung-Chun Yang
en Limba Engleză Paperback – 8 oct 2011
For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for­ mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func­ tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur­ 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.
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Specificații

ISBN-13: 9781441952431
ISBN-10: 1441952438
Pagini: 480
Ilustrații: IX, 467 p.
Dimensiuni: 160 x 240 x 25 mm
Greutate: 0.67 kg
Ediția:2003
Editura: Springer Us
Colecția Springer
Seria Advances in Complex Analysis and Its Applications

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

1 Nevanlinna theory.- 2 Uniqueness of meromorphic functions on ?.- 3 Uniqueness of meromorphic functions on ?m.- 4 Uniqueness of meromorphic mappings.- 5 Algebroid functions of several variables.- References.- Symbols.