JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON UNIVERSAL FUNCTIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON UNIVERSAL FUNCTIONS
Aron, Richard; Markose, Dinesh;
  PDF(new window)
 Abstract
An entire function is called universal with respect to translations if for any $g\;{\in}\;H(\mathbb{C}),\;R\;>\;0,\;and\;{\epsilon}\;>\;0$, there is such that $f(z\;+\;n)\;-\;g(z)\;<\;{\epsilon}$ whenever $z\;{\leq}\;R$. Similarly, it is universal with respect to differentiation if for any g, R, and , there is n such that $f^{(n)}(z)\;-\;g(z)\;<\;{\epsilon}\;for\;z\;{\leq}\;R$. In this note, we review G. MacLane's proof of the existence of universal functions with respect to differentiation, and we give a simplified proof of G. D. Birkhoff's theorem showing the existence of universal functions with respect to translation. We also discuss Godefroy and Shapiro's extension of these results to convolution operators as well as some new, related results and problems.
 Keywords
hypercyclic;analytic functions;convolution operators;
 Language
English
 Cited by
1.
PDE-PRESERVING PROPERTIES,;

대한수학회지, 2005. vol.42. 3, pp.573-597 crossref(new window)
2.
HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM,;

대한수학회보, 2007. vol.44. 1, pp.117-123 crossref(new window)
1.
Remarks on a result about hypercyclic non-convolution operators, Journal of Mathematical Analysis and Applications, 2005, 309, 1, 52  crossref(new windwow)
2.
On Linear Dynamics in Quantum Calculus, Results in Mathematics, 2014, 65, 3-4, 415  crossref(new windwow)
3.
Hypercyclic sequences of PDE-preserving operators, Journal of Approximation Theory, 2006, 138, 2, 168  crossref(new windwow)
4.
Commutation relations and hypercyclic operators, Archiv der Mathematik, 2012, 99, 3, 247  crossref(new windwow)
5.
Convolution operators supporting hypercyclic algebras, Journal of Mathematical Analysis and Applications, 2017, 445, 2, 1232  crossref(new windwow)
6.
Hypercyclic convolution operators on Fréchet spaces of analytic functions, Journal of Mathematical Analysis and Applications, 2007, 336, 2, 1324  crossref(new windwow)
7.
An Extension of Hypercyclicity forN-Linear Operators, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
8.
Fixed points and orbits of non-convolution operators, Fixed Point Theory and Applications, 2014, 2014, 1, 221  crossref(new windwow)
9.
On the universality of multipliers on H(C), Journal of Approximation Theory, 2010, 162, 5, 1025  crossref(new windwow)
10.
Universality properties of the quaternionic power series and entire functions, Mathematische Nachrichten, 2015, 288, 8-9, 917  crossref(new windwow)
11.
Rate of Growth of Hypercyclic and Frequently Hypercyclic Functions for the Dunkl Operator, Mediterranean Journal of Mathematics, 2016, 13, 5, 3359  crossref(new windwow)
12.
S-Mixing Tuple of Operators on Banach Spaces, Journal of Function Spaces, 2016, 2016, 1  crossref(new windwow)
13.
Dynamics of the Basic Bessel Operator and Related Convolution Operators on Spaces of Entire Functions, Complex Analysis and Operator Theory, 2015, 9, 1, 167  crossref(new windwow)
14.
RETRACTED ARTICLE: Convolution Operators Associated with the Generalized Airy Operator on the Complex Plane, Complex Analysis and Operator Theory, 2016, 10, 1, 231  crossref(new windwow)
 References
1.
Contemp. Math., 1998. vol.232. pp.39-46

2.
C. R. Acad. Sci. Paris, 1929. vol.189. pp.473-475

3.
Enseign. Math., 1984. vol.30. 2;3-4, pp.269-274

4.
Ann. Inst. Foyrier (Grenoble), 1949. vol.I. pp.61-101

5.
Proc. Amer. Math. Soc., 1987. vol.100. 2, pp.281-288 crossref(new window)

6.
J. Funct. Anal., 1991. vol.98. 2, pp.229-269 crossref(new window)

7.
Nederl. Akad. Wetensch. Proc. Ser. A73, Indag. Math., 1970. vol.32. pp.356-358

8.
Dissertation, Univ. Toronto, 1982.

9.
J. Anal. Math., 1952. vol.2. pp.72-87 crossref(new window)

10.
Ann. Inst. Fourier (Grenoble), 1955. vol.VI. pp.271-355

11.
Ann. Math. Blaise Pascal, 2001. vol.8. 2, pp.107-114 crossref(new window)