Functions Belonging to a Dirichlet Subalgebra of the Disk Algebra
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 375-377

Voir la notice de l'article provenant de la source Cambridge University Press

Browder and Wermer in [2] give a method for constructing Dirichlet subalgebras of the disk algebra. In this note we show that these Dirichlet algebras do not contain any non-constant functions which satisfy a Lipschitz-one condition on a subinterval of the unit circle.
Lund, Bruce. Functions Belonging to a Dirichlet Subalgebra of the Disk Algebra. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 375-377. doi: 10.4153/CMB-1975-068-5
@article{10_4153_CMB_1975_068_5,
     author = {Lund, Bruce},
     title = {Functions {Belonging} to a {Dirichlet} {Subalgebra} of the {Disk} {Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {375--377},
     year = {1975},
     volume = {18},
     number = {3},
     doi = {10.4153/CMB-1975-068-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-068-5/}
}
TY  - JOUR
AU  - Lund, Bruce
TI  - Functions Belonging to a Dirichlet Subalgebra of the Disk Algebra
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 375
EP  - 377
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-068-5/
DO  - 10.4153/CMB-1975-068-5
ID  - 10_4153_CMB_1975_068_5
ER  - 
%0 Journal Article
%A Lund, Bruce
%T Functions Belonging to a Dirichlet Subalgebra of the Disk Algebra
%J Canadian mathematical bulletin
%D 1975
%P 375-377
%V 18
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-068-5/
%R 10.4153/CMB-1975-068-5
%F 10_4153_CMB_1975_068_5

[1] 1. Blumenthal, R. G., Maximality in function algebras, Canad. J. Math. 22 (1970), 1002-1004. Google Scholar

[2] 2. Browder, A. and Wermer, J., A method of constructing Dirichlet algebras, Proc. Amer. Math. Soc. 15 (1964), 546-552. Google Scholar

[3] 3. Duren, P. L., Theory of Hp Spaces, Academic Press, New York, 1970. Google Scholar

[4] 4. Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962. Google Scholar

[5] 5. Serrin, J. and Varberg, D. E., A general chain rule for derivatives and the change of variables formula for the Lebesgue integral, Amer. Math. Monthly 76 (1969), 514-520. Google Scholar

[6] 6. Stout, E. L., The Theory of Uniform Algebras, Bogden and Quigley, Tarrytown on Hudson, N.Y., (1971). Google Scholar

Cité par Sources :