On the coefficient bodies of meromorphic univalent functions omitting a disc

Olli Tammi

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 1, page 47-58
  • ISSN: 0066-2216

Abstract

top
Let S(b) be the class of bounded normalized univalent functions and Σ(b) the class of normalized univalent meromorphic functions omitting a disc with radius b. The close connection between these classes allows shifting the coefficient body information from the former to the latter. The first non-trivial body can be determined in Σ(b) as well as the next one in the real subclass Σ R ( b ) .

How to cite

top

Tammi, Olli. "On the coefficient bodies of meromorphic univalent functions omitting a disc." Annales Polonici Mathematici 75.1 (2000): 47-58. <http://eudml.org/doc/208383>.

@article{Tammi2000,
abstract = {Let S(b) be the class of bounded normalized univalent functions and Σ(b) the class of normalized univalent meromorphic functions omitting a disc with radius b. The close connection between these classes allows shifting the coefficient body information from the former to the latter. The first non-trivial body can be determined in Σ(b) as well as the next one in the real subclass $Σ_\{R\}(b)$.},
author = {Tammi, Olli},
journal = {Annales Polonici Mathematici},
keywords = {coefficient bodies; univalent functions},
language = {eng},
number = {1},
pages = {47-58},
title = {On the coefficient bodies of meromorphic univalent functions omitting a disc},
url = {http://eudml.org/doc/208383},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Tammi, Olli
TI - On the coefficient bodies of meromorphic univalent functions omitting a disc
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 47
EP - 58
AB - Let S(b) be the class of bounded normalized univalent functions and Σ(b) the class of normalized univalent meromorphic functions omitting a disc with radius b. The close connection between these classes allows shifting the coefficient body information from the former to the latter. The first non-trivial body can be determined in Σ(b) as well as the next one in the real subclass $Σ_{R}(b)$.
LA - eng
KW - coefficient bodies; univalent functions
UR - http://eudml.org/doc/208383
ER -

References

top
  1. [1] Charzyński, Z.: and Janowski, W.:, Domaine de variation des coefficients A 2 et A 3 des functions univalentes et bornées, Bull. Soc. Sci. Lettres Łódź 10 (1959), no. 5. Zbl0227.30016
  2. [2] Jokinen, O.: and Tammi, O.:, On determining the points of the second coefficient body ( a 4 , a 3 , a 2 ) for bounded real univalent functions, Kodai Math. J. 17 (1994), 82-100. Zbl0805.30013
  3. [3] Kortram, R.: and Tammi, O.:, On the first coefficient regions of bounded univalent functions, Ann. Acad. Sci. Fenn. Ser. A I 592 (1974). Zbl0305.30019
  4. [4] Netanyahu, E.:, Extremal problems for schlicht functions in the exterior of the unit circle, Canad. J. Math. 17 (1965), 335-341. Zbl0148.30804
  5. [5] Schaeffer, A. C. : and Spencer, D. C.:, Coefficient Regions for Schlicht Functions, Amer. Math. Soc. Colloq. Publ. 35, 1950. 
  6. [6] Siejka, H.:, On meromorphic univalent functions omitting a disc, Israel J. Math. 54 (1986), 291-299. Zbl0608.30020
  7. [7] Śladkowska, J.:, Estimations of the second coefficient of a univalent, bounded, symmetric and non-vanishing function by means of Loewner's parametric method, Ann. Polon. Math. 68 (1998), 119-123. Zbl0905.30012
  8. [8] Tammi, O.:, Extremum Problems for Bounded Univalent Functions, Lecture Notes in Math. 646, Springer, Berlin, 1978. Zbl0375.30006
  9. [9] Tammi, O.: Extremum Problems for Bounded Univalent Functions II, Lecture Notes in Math. 913, Springer, Berlin, 1982. Zbl0481.30020
  10. [10] Tammi, O.: On the first coefficient bodies of bounded real non-vanishing univalent functions, Ann. Univ. Mariae Curie-Skłodowska 52 (1998), 177-190. Zbl1009.30012

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.