Derivative and antiderivative operators and the size of complex domains

Luis Bernal-González

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 3, page 267-274
  • ISSN: 0066-2216

Abstract

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We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.

How to cite

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Luis Bernal-González. "Derivative and antiderivative operators and the size of complex domains." Annales Polonici Mathematici 59.3 (1994): 267-274. <http://eudml.org/doc/262351>.

@article{LuisBernal1994,
abstract = {We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.},
author = {Luis Bernal-González},
journal = {Annales Polonici Mathematici},
keywords = {universal function; equicontinuous sequence; derivative operator; antiderivative operator; MacLane's theorem; size of a domain; existence of universal functions; space of holomorphic functions; equicontinuity},
language = {eng},
number = {3},
pages = {267-274},
title = {Derivative and antiderivative operators and the size of complex domains},
url = {http://eudml.org/doc/262351},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Luis Bernal-González
TI - Derivative and antiderivative operators and the size of complex domains
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 3
SP - 267
EP - 274
AB - We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.
LA - eng
KW - universal function; equicontinuous sequence; derivative operator; antiderivative operator; MacLane's theorem; size of a domain; existence of universal functions; space of holomorphic functions; equicontinuity
UR - http://eudml.org/doc/262351
ER -

References

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  1. [1] C. Blair and L. A. Rubel, A universal entire function, Amer. Math. Monthly 90 (1983), 331-332. Zbl0534.30029
  2. [2] C. Blair and L. A. Rubel, A triply universal entire function, Enseign. Math. 30 (1984), 269-274. Zbl0559.30033
  3. [3] S. M. Duios Ruis, Universal functions of the structure of the space of entire functions, Soviet Math. Dokl. 30 (1984), 713-716. 
  4. [4] R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), 281-288. Zbl0618.30031
  5. [5] G. Godefroy and J. H. Shapiro, Operators with dense, invariants, cyclic vector manifolds, J. Funct. Anal. 98 (1991), 229-269. Zbl0732.47016
  6. [6] K. G. Grosse-Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giessen 176 (1987). 
  7. [7] K. G. Grosse-Erdmann, On the universal functions of G. R. MacLane, Complex Variables Theory Appl. 15 (1990), 193-196. Zbl0682.30021
  8. [8] J. Horváth, Topological Vector Spaces, Vol. 1, Addison-Wesley, Reading, 1966. 
  9. [9] W. Luh, Approximation by antiderivatives, Constr. Approx. 2 (1986), 179-187. Zbl0615.30034
  10. [10] G. R. MacLane, Sequences of derivatives and normal families, J. Analyse Math. 2 (1952), 72-87. Zbl0049.05603
  11. [11] J. C. Oxtoby, Measure and Category, 2nd ed., Springer, New York, 1980. Zbl0435.28011
  12. [12] W. Rudin, Real and Complex Analysis, 2nd ed., Tata McGraw-Hill, Faridabad, 1974. Zbl0278.26001

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