The Schwarz-Pick theorem and its applications

M. A. Qazi; Q. I. Rahman

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2011)

  • Volume: 65, Issue: 2
  • ISSN: 0365-1029

Abstract

top
Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.

How to cite

top

M. A. Qazi, and Q. I. Rahman. "The Schwarz-Pick theorem and its applications." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 65.2 (2011): null. <http://eudml.org/doc/289732>.

@article{M2011,
abstract = {Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.},
author = {M. A. Qazi, Q. I. Rahman},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Bernstein’s inequality; functions of exponential type in a half-plane; rational functions; Schwarz-Pick theorem},
language = {eng},
number = {2},
pages = {null},
title = {The Schwarz-Pick theorem and its applications},
url = {http://eudml.org/doc/289732},
volume = {65},
year = {2011},
}

TY - JOUR
AU - M. A. Qazi
AU - Q. I. Rahman
TI - The Schwarz-Pick theorem and its applications
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2011
VL - 65
IS - 2
SP - null
AB - Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.
LA - eng
KW - Bernstein’s inequality; functions of exponential type in a half-plane; rational functions; Schwarz-Pick theorem
UR - http://eudml.org/doc/289732
ER -

References

top
  1. Ahlfors, L. V., Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill Book Company, New York-Dusseldorf-Johannesburg, 1973. 
  2. Bernstein, S. N., Sur la limitation des derivees des polynomes, C. R. Math. Acad. Sci. Paris 190 (1930), 338-340. 
  3. Boas, Jr., R. P., Entire Functions, Academic Press, New York, 1954. 
  4. Caratheodory, C., Conformal Representation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 28, Cambridge University Press, Cambridge, 1963. 
  5. Krzyż, J. G., Problems in Complex Variable Theory, American Elsevier Publishing Company, Inc., New York, 1971. 
  6. Qazi, M. A., Rahman, Q. I., Some estimates for the derivatives of rational functions, Comput. Methods Funct. Theory 10 (2010), 61-79. 
  7. Qazi, M. A., Rahman, Q. I., Functions of exponential type in a half-plane, Complex Var. Elliptic Equ. (in print). 
  8. Rahman, Q. I., Inequalities concerning polynomials and trigonometric polynomials, J. Math. Anal. Appl. 6 (1963), 303-324. 
  9. Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002. 

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.