# 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

top- [Ga] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
- [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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