The Maximum Number of Zeros of r(z)-z¯ Revisited

Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions f ( z ) = p ( z ) q ( z ) - z ¯ , which depend on both deg ( p ) and deg ( q ) . Furthermore, we prove that any function that attains one of these uppe...

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Vydáno v:Computational methods and function theory Ročník 18; číslo 3; s. 463 - 472
Hlavní autoři: Liesen, Jörg, Zur, Jan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2018
Springer Nature B.V
Témata:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Harmonic functions
Mathematics
Mathematics and Statistics
Upper bounds
Rational harmonic functions
Complex valued harmonic functions
Harmonic polynomials
Zeros of rational harmonic functions
30D05
37F10
31A05
ISSN:1617-9447, 2195-3724
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Popis
Shrnutí:Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions f ( z ) = p ( z ) q ( z ) - z ¯ , which depend on both deg ( p ) and deg ( q ) . Furthermore, we prove that any function that attains one of these upper bounds is regular.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-017-0231-1