On two new functional equations for generalized Joukowski transformations

M. Baran; H. Haruki

Annales Polonici Mathematici (1991)

  • Volume: 56, Issue: 1, page 79-85
  • ISSN: 0066-2216

Abstract

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The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function 1 / 2 ( z + z - 1 ) of a complex variable z.

How to cite

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M. Baran, and H. Haruki. "On two new functional equations for generalized Joukowski transformations." Annales Polonici Mathematici 56.1 (1991): 79-85. <http://eudml.org/doc/262332>.

@article{M1991,
abstract = {The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function $1/2 (z + z^\{-1\})$ of a complex variable z.},
author = {M. Baran, H. Haruki},
journal = {Annales Polonici Mathematici},
keywords = {Joukowski transformations; meromorphic functions; Picard's and Riemann's theorem; removable singularities; general solution},
language = {eng},
number = {1},
pages = {79-85},
title = {On two new functional equations for generalized Joukowski transformations},
url = {http://eudml.org/doc/262332},
volume = {56},
year = {1991},
}

TY - JOUR
AU - M. Baran
AU - H. Haruki
TI - On two new functional equations for generalized Joukowski transformations
JO - Annales Polonici Mathematici
PY - 1991
VL - 56
IS - 1
SP - 79
EP - 85
AB - The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function $1/2 (z + z^{-1})$ of a complex variable z.
LA - eng
KW - Joukowski transformations; meromorphic functions; Picard's and Riemann's theorem; removable singularities; general solution
UR - http://eudml.org/doc/262332
ER -

References

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  1. [1] J. Aczél, Review for [6], Zentralblatt für Math. 139 (1968), 97. 
  2. [2] J. Aczél and H. Haruki, Commentaries on Hille's papers. Chapter 1. Functional equations, in: E. Hille, Classical Analysis and Functional Analysis. Selected Papers, R. Kallman (ed.), MIT Press, Cambridge, Mass., 1975, 651-658. 
  3. [3] L. V. Ahlfors, Complex Analysis, 2nd ed., McGraw-Hill, 1966. 
  4. [4] M. Baran, Siciak’s extremal function of convex sets in N , Ann. Polon. Math. 48 (1988), 275-280. Zbl0661.32023
  5. [5] M. Baran, A functional equation for the Joukowski transformation, Proc. Amer. Math. Soc. 105 (1989), 423-427. Zbl0676.39003
  6. [6] H. Haruki, Studies on certain functional equations from the standpoint of analytic function theory, Sci. Rep. Osaka Univ. 14 (1965), 1-40. Zbl0139.09703
  7. [7] H. Haruki, A functional equation arising from the Joukowski transformation, Ann. Polon. Math. 45 (1985), 185-191. Zbl0577.30037
  8. [8] H. Haruki, A new functional equation characterizing generalized Joukowski transformations, Aequationes Math. 32 (1987), 327-335. Zbl0618.39004
  9. [9] G. Salmon, A Treatise on Conic Sections, Chelsea Publ. Co., New York 1957. 

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