Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-07T19:21:59.167Z Has data issue: false hasContentIssue false

Category Results for Tsuji Functions

Published online by Cambridge University Press:  20 November 2018

D. D. Bonar
Affiliation:
Denison University, Granville, Ohio
F. W. Carroll
Affiliation:
Denison University, Granville, Ohio
Peter Colwell
Affiliation:
Denison University, Granville, Ohio
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let D be the unit disk, |z| < 1, and H(D) the Fréchet space of holomorphic functions on D, provided with the topology of uniform convergence on compact subsets of D. If f is meromorphic in D, we denote by

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Anderson, J. M., Category theorems for certain Banach spaces of analytic functions, J. Reine Angew. Math. 249 (1971), 8391.Google Scholar
2. Bagemihl, F., Tsuji points and Tsuji functions, Comment. Math. Univ. St. Paul 17 (1968), 1720.Google Scholar
3. Bagemihl, F. and Erdos, P., A problem concerning the zeros of a certain kind of holomorphic function in the unit disk, J. Reine Angew. Math. 214/215 (1964), 340344.Google Scholar
4. Banach, S., Opérations linéaires (Chelsea, N.Y.).Google Scholar
5. Bonar, D. D., On annular function, VEB Deutscher Verlag der Wissenschaften, Berlin, 1971.Google Scholar
6. Bonar, D. D. and Carroll, F. W., Annular functions form a residual set, J. Reine Angew. Math. 272 (1975), 2324.Google Scholar
7. Brown, L. and Hansen, L., On the range sets of Hp functions, Pacific J. Math. 42 (1972), 2732.Google Scholar
8. Collingwood, E. F. and Lohwater, A. J., The theory of cluster sets, (Cambridge University Press, London 1966).Google Scholar
9. Collingwood, E. F. and Piranian, G., Tsuji functions with segments of Julia, Math. Z. 84 (1964), 246253.Google Scholar
10. Cohvell, P., A category theorem for Tsuji functions, Proc. A.M.S. 51 (1975), 344346.Google Scholar
11. Hayman, W. K., The boundary behaviour of Tsuji functions, Mich. Math. J. 15 (1968), 126.Google Scholar
12. Howell, R. W., Annular functions and residual sets, Proc. A.M.S. 52 (1975), 217221.Google Scholar
13. McMillan, J. E., Principal cluster values of continuous functions, Math. Z. 91 (1966), 186197.Google Scholar
14. Taylor, A. E., Functional analysis (Wiley, New York).Google Scholar
15. Tsuji, M., A theorem on the boundary behaviour of a meromorphic function in \z\ < 1, Comment. Math. Univ. St. Paul 8 (1960), 5355.Google Scholar