Homogeneous algebras on the circle. I: Ideals of analytic functions. (English) Zbl 0228.46046


46J10 Banach algebras of continuous functions, function algebras
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
46J20 Ideals, maximal ideals, boundaries
Full Text: DOI Numdam EuDML


[1] L. AHLFORS and M. HEINS, Questions of regularity connected with the phragmen-Lindelöf principle, Ann. of Math., (2) 50 (1949), 341-346. · Zbl 0036.04702
[2] C. BENNETT, On the harmonic analysis of rearrangement-invariant Banach function spaces, Thesis, University of Newcastle, 1971.
[3] R.P. BOAS, “entire functions”, Academic Press (1954), New York. · Zbl 0058.30201
[4] T. CARLEMAN, “L”intégrale de Fourier et questions qui s’y rattachent”, Almqvist and Wiksell (1944), Uppsala. · Zbl 0060.25504
[5] Y. DOMAR, On the existence of a largest subharmonic minorant of a given function, Ark. Mat. 3, (1967), 429-440. · Zbl 0078.09301
[6] J.E. GILBERT, On the harmonic analysis of some subalgebras of L1 (0, ∞), Seminar, Symposium in Harmonic Analysis, Warwick (1968).
[7] V.P. GURARII, On primary ideals in the space L1 (0, ∞), Soviet Math. Doklady, 7 (1966), 266-268. · Zbl 0154.39203
[8] M. HASUMI and T. SRINIVASAN, Invariant subspaces of analytic functions, Canad. J. Math., 17 (1965), 643-651. · Zbl 0128.34201
[9] K. HOFFMAN, “banach spaces of analytic functions”, Prentice-Hall (1962), Englewood Cliffs, N.J. · Zbl 0117.34001
[10] J.P. KAHANE, Idéaux primaires fermés dans certaines algèbres de Banach de fonctions analytiques, (to appear). · Zbl 0271.46047
[11] Y. KATZNELSON, “an introduction to harmonic analysis”, John Wiley (1968), New York. · Zbl 0169.17902
[12] P. KOOSIS, On the spectral analysis of bounded functions, Pacific J. Math., 16 (1966), 121-128. · Zbl 0146.12201
[13] B.I. KORENBLYUM, A generalization of Wiener’s Tauberian theorem and spectrum of fast growing functions, Trudy Moskov Mat. Obsc., 7 (1958), 121-148.
[14] K. de LEEUW, Homogeneous algebras on compact abelian groups, Trans. Amer. Math. Soc., 87 (1958), 372-386. · Zbl 0083.34603
[15] H. MIRKIL, The work of silov on commutative Banach algebras, Notas de Matematica, No. 20 (1959), Rio de Janeiro. · Zbl 0090.09301
[16] B. NYMAN, On the one-dimensional translation group and semi-group in certain function spaces, Thesis (1950), Uppsala. · Zbl 0037.35401
[17] W. RUDIN, Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc., 8 (1957), 39-42. · Zbl 0077.31103
[18] G.E. SILOV, Homogeneous rings of functions, Amer. Math. Soc. Translation No. 92. · Zbl 0053.08401
[19] B.A. TAYLOR and D.L. WILLIAMS, The space of functions analytic in the disk with indefinitely differentiable boundary values, (submitted for publication).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.