A constructive proof of the Beurling-Rudin theorem
Studia Mathematica (1998)
- Volume: 129, Issue: 1, page 51-58
- ISSN: 0039-3223
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topMortini, Raymond. "A constructive proof of the Beurling-Rudin theorem." Studia Mathematica 129.1 (1998): 51-58. <http://eudml.org/doc/216491>.
@article{Mortini1998,
abstract = {A constructive proof of the Beurling-Rudin theorem on the characterization of the closed ideals in the disk algebra A(𝔻) is given.},
author = {Mortini, Raymond},
journal = {Studia Mathematica},
keywords = {Blaschke product; disk algebra; elementary and constructive proof; Beurling-Rudin theorem; closed ideal; greatest common divisor of the normalized inner factors; peak function; inner factor of the sum of two inner functions},
language = {eng},
number = {1},
pages = {51-58},
title = {A constructive proof of the Beurling-Rudin theorem},
url = {http://eudml.org/doc/216491},
volume = {129},
year = {1998},
}
TY - JOUR
AU - Mortini, Raymond
TI - A constructive proof of the Beurling-Rudin theorem
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 1
SP - 51
EP - 58
AB - A constructive proof of the Beurling-Rudin theorem on the characterization of the closed ideals in the disk algebra A(𝔻) is given.
LA - eng
KW - Blaschke product; disk algebra; elementary and constructive proof; Beurling-Rudin theorem; closed ideal; greatest common divisor of the normalized inner factors; peak function; inner factor of the sum of two inner functions
UR - http://eudml.org/doc/216491
ER -
References
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- [Ho] K. Hoffman, Banach Spaces of Analytic Functions, Dover Publ., New York, 1988 (reprint of the 1962 edition).
- [Mo] R.Mortini, Closed and prime ideals in the algebra of bounded analytic functions, Bull. Austral. Math. Soc. 35 (1987) 213-229. Zbl0601.46052
- [MoRu] R. Mortini and R. Rupp, A constructive proof of the Nullstellensatz for subalgebras of A(K), Trav. Math. 3, Publ. CUL, 1991, 45-49. Zbl0735.30040
- [vR] M. von Renteln, A simple constructive proof of an analogue of the Corona theorem, Proc. Amer. Math. Soc. 83 (1981) 299-303. Zbl0479.30037
- [Ru] W. Rudin, The closed ideals in an algebra of analytic functions, Canad. Math. J. 9 (1957) 426-434. Zbl0080.31703
- [Rud] W. Rudin, A generalization of a theorem of Frostman, Math. Scand. 21 (1967), 136-143. Zbl0185.33301
- [SrWa] T. P. Srinivasan and J. K. Wang, On the closed ideals of analytic functions, Proc. Amer. Math. Soc. 16 (1965), 49-52. Zbl0143.15504
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