Faber polynomials

In mathematics, the Faber polynomials P_m of a Laurent series

: $\displaystyle f(z)=z^{-1}+a_0+a_1z+\cdots$

are the polynomials such that

: $\displaystyle P_m(f)-z^{-m}$

vanishes at z=0. They were introduced by {{harvs |txt |last=Faber |authorlink=Georg Faber |year1=1903 |year2=1919}} and studied by {{harvs|txt|last=Grunsky|authorlink=Helmut Grunsky|year=1939}} and {{harvs|txt|last=Schur|authorlink=Issai Schur|year=1945}}.

References

{{Citation | last1=Curtiss | first1=J. H. | title=Faber Polynomials and the Faber Series | jstor=2316567 | publisher=Mathematical Association of America | year=1971 | journal=The American Mathematical Monthly | issn=0002-9890 | volume=78 | issue=6 | pages= 577–596 | doi=10.2307/2316567}}
{{Citation | last1=Faber | first1=Georg | title=Über polynomische Entwickelungen | doi=10.1007/BF01444293 | publisher=Springer Berlin / Heidelberg | year=1903 | journal=Mathematische Annalen | issn=0025-5831 | volume=57 | issue=3 | pages=389–408| url=https://zenodo.org/record/2129496 }}
{{Citation | last1=Faber | first1=G. | title=Über Tschebyscheffsche Polynome. | url=http://resolver.sub.uni-goettingen.de/purl?GDZPPN00216874X | language=German | jfm=47.0315.01 | year=1919 | journal=Journal für die reine und angewandte Mathematik | issn=0075-4102 | volume=150 | pages=79–106}}
{{Citation | last1=Grunsky | first1=Helmut | title=Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen | doi=10.1007/BF01580272 | year=1939 | journal=Mathematische Zeitschrift | issn=0025-5874 | volume=45 | issue=1 | pages=29–61}}
{{Citation | last1=Schur | first1=Issai | title=On Faber polynomials | jstor=2371913 | mr=0011740 | year=1945 | journal=American Journal of Mathematics | issn=0002-9327 | volume=67 | issue=1 | pages=33–41 | doi=10.2307/2371913}}
{{Citation | last1=Suetin | first1=P. K. | title=Series of Faber polynomials | orig-date=1984 | url=https://books.google.com/books?id=uZZS0Eeh5RMC | publisher=Gordon and Breach Science Publishers | location=New York | series=Analytical Methods and Special Functions | isbn=978-90-5699-058-9 | mr=1676281 | year=1998 | volume=1}}
{{eom|title=Faber polynomials|first=P. K.|last= Suetin}}

Category:Polynomials