|
Algebras of functions on the unit circle
Author:
Donald Sarason
Journal:
Bull. Amer. Math. Soc. 79 (1973), 286-299
MSC (1970):
Primary 46J10, 30A76, 30A78
MathSciNet review:
0324425
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
Ralph
Philip Boas Jr., Entire functions, Academic Press Inc., New
York, 1954. MR
0068627 (16,914f)
- 2.
Lennart
Carleson, Interpolations by bounded analytic functions and the
corona problem, Ann. of Math. (2) 76 (1962),
547–559. MR 0141789
(25 #5186)
- 3.
Paul
J. Cohen, A note on constructive methods in
Banach algebras, Proc. Amer. Math. Soc. 12 (1961), 159–163.
MR
0124515 (23 #A1827), http://dx.doi.org/10.1090/S0002-9939-1961-0124515-4
- 4.
A.
M. Davie, T.
W. Gamelin, and J.
Garnett, Distance estimates and pointwise
bounded density, Trans. Amer. Math. Soc. 175 (1973), 37–68.
MR
0313514 (47 #2068), http://dx.doi.org/10.1090/S0002-9947-1973-0313514-8
- 5.
R.
G. Douglas, Toeplitz and Wiener-Hopf operators in
𝐻^{∞}+𝐶, Bull. Amer.
Math. Soc. 74
(1968), 895–899. MR 0229070
(37 #4648), http://dx.doi.org/10.1090/S0002-9904-1968-12071-3
- 6.
R.
G. Douglas, On the spectrum of Toeplitz and Wiener-Hopf
operators, Abstract Spaces and Approximation (Proc. Conf.,
Oberwolfach, 1968) Birkhäuser, Basel, 1969, pp. 53–66. MR 0259638
(41 #4274)
- 7.
R.
G. Douglas and Walter
Rudin, Approximation by inner functions, Pacific J. Math.
31 (1969), 313–320. MR 0254606
(40 #7814)
- 8.
R.
G. Douglas and Donald
Sarason, Fredholm Toeplitz operators,
Proc. Amer. Math. Soc. 26 (1970), 117–120. MR 0259639
(41 #4275), http://dx.doi.org/10.1090/S0002-9939-1970-0259639-X
- 9.
R.
G. Douglas and Donald
Sarason, A class of Toeplitz operators, Proceedings of an
International Symposium on Operator Theory (Indiana Univ., Bloomington,
Ind., 1970), 1971, pp. 891–895. MR 0407642
(53 #11414)
- 10.
C. Fefferman and E. M. Stein, (in preparation).
- 11.
John
Garnett and Irving
Glicksberg, Algebras with the same multiplicative measures, J.
Functional Analysis 1 (1967), 331–341. MR 0217602
(36 #691)
- 12.
Andrew
M. Gleason and Hassler
Whitney, The extension of linear functionals defined on
𝐻^{∞}, Pacific J. Math. 12 (1962),
163–182. MR 0142013
(25 #5408)
- 13.
Henry
Helson, Lectures on invariant subspaces, Academic Press, New
York, 1964. MR
0171178 (30 #1409)
- 14.
Henry
Helson and Donald
Sarason, Past and future, Math. Scand 21
(1967), 5–16 (1968). MR 0236989
(38 #5282)
- 15.
Kenneth
Hoffman, Banach spaces of analytic functions, Prentice-Hall
Series in Modern Analysis, Prentice-Hall Inc., Englewood Cliffs, N. J.,
1962. MR
0133008 (24 #A2844)
- 16.
K.
Hoffman and I.
M. Singer, Maximal algebras of continuous functions, Acta
Math. 103 (1960), 217–241. MR 0117540
(22 #8318)
- 17.
Z.
L. Leĭbenzon, On the ring of continuous functions on a
circle, Uspehi Matem. Nauk (N.S.) 7 (1952),
no. 4(50), 163–164 (Russian). MR 0050809
(14,386a)
- 18.
G.
Lumer, Analytic functions and Dirichlet
problem, Bull. Amer. Math. Soc. 70 (1964), 98–104. MR 0158283
(28 #1509), http://dx.doi.org/10.1090/S0002-9904-1964-11036-3
- 19.
G.
Lumer, On Wermer’s maximality theorem, Invent. Math.
8 (1969), 236–237. MR 0251542
(40 #4769)
- 20.
Donald
Sarason, Generalized interpolation in
𝐻^{∞}, Trans. Amer. Math.
Soc. 127 (1967),
179–203. MR 0208383
(34 #8193), http://dx.doi.org/10.1090/S0002-9947-1967-0208383-8
- 21.
Donald
Sarason, An addendum to: “Past and future” (Math.
Scand. 21 (1967), 5–16 (1968)) by H. Helson and D. Sarason,
Math. Scand. 30 (1972), 62–64. MR 0385990
(52 #6849)
- 22.
Donald
Sarason, On products of Toeplitz operators, Acta Sci. Math.
(Szeged) 35 (1973), 7–12. MR 0331109
(48 #9443)
- 22.
D. Sarason, Invariant subspaces (to appear).
- 24.
Donald
Sarason, Approximation of piecewise continuous functions by
quotients of bounded analytic functions, Canad. J. Math.
24 (1972), 642–657. MR 0310647
(46 #9745)
- 25.
Wladimir
Seidel, On the distribution of values of
bounded analytic functions, Trans. Amer. Math.
Soc. 36 (1934), no. 1, 201–226. MR
1501738, http://dx.doi.org/10.1090/S0002-9947-1934-1501738-9
- 27.
John
Wermer, On algebras of continuous
functions, Proc. Amer. Math. Soc. 4 (1953), 866–869. MR 0058877
(15,440g), http://dx.doi.org/10.1090/S0002-9939-1953-0058877-9
- 28.
Lawrence
Zalcman, Bounded analytic functions on domains
of infinite connectivity, Trans. Amer. Math.
Soc. 144 (1969),
241–269. MR 0252665
(40 #5884), http://dx.doi.org/10.1090/S0002-9947-1969-0252665-2
- 1.
- R. P. Boas, Jr., Entire functions, Academic Press, New York, 1954. MR 16, 914. MR 68627
- 2.
- L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547-559. MR 25 #5186. MR 141789
- 3.
- P. J. Cohen, A note on constructive methods in Banach algebras, Proc. Amer. Math. Soc. 12 (1961), 159-163. MR 23 # A1827. MR 124515
- 4.
- A. M. Davie, T. W. Gamelin and J. Garnett, Distance estimates and pointwise bounded density (to appear). MR 313514
- 5.
- R. G. Douglas, Toeplitz and Wiener-Hopf operators in H∞ + C, Bull. Amer. Math. Soc. 74 (1968), 895-899. MR 37 #4648. MR 229070
- 6.
- R. G. Douglas, On the spectrum of Toeplitz and Wiener-Hopf operators, Abstract Spaces and Approximation (Proc. Conf., Oberwolfach, 1968), Birkhäuser, Basel, 1969, pp. 53-66. MR 41 #4274. MR 259638
- 7.
- R. G. Douglas and W. Rudin, Approximation by inner functions, Pacific J. Math. 31 (1969), 313-320. MR 40 #7814. MR 254606
- 8.
- R. G. Douglas and D. Sarason, Fredholm Toeplitz operators, Proc. Amer. Math. Soc. 26 (1970), 117-120. MR 41 #4275. MR 259639
- 9.
- R. G. Douglas and D. Sarason, A class of Toeplitz operators, Indiana Univ. Math. J. 20 (1971), 891-895. MR 407642
- 10.
- C. Fefferman and E. M. Stein, (in preparation).
- 11.
- J. Garnett and I. Glicksberg, Algebras with the same multiplicative measures, J. Functional Analysis 1 (1967), 331-341. MR 36 #691. MR 217602
- 12.
- A. M. Gleason and H. Whitney, The extension of linear functionals on H∞, Pacific J. Math. 12 (1962), 163-182. MR 25 #5408. MR 142013
- 13.
- H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964. MR 30 #1409. MR 171178
- 14.
- H. Helson and D. Sarason, Past and future, Math. Scand. 21 (1967), 5-16. MR 38 #5282. MR 236989
- 15.
- K. Hoffman, Banach spaces of analytic functions, Prentice-Hall Ser. in Modern Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1962. MR 24 #A2844. MR 133008
- 16.
- K. Hoffman and I. M. Singer, Maximal algebras of continuous functions, Acta Math. 103 (1960), 217-241. MR 22 #8318. MR 117540
- 17.
- Z. L. Leìbenzon, On the ring of continuous functions on a circle, Uspehi Mat. Nauk 7 (1952), no. 4 (50), 163-164. (Russian) MR 14, 386. MR 50809
- 18.
- G. Lumer, Analytic functions and Dirichlet problem, Bull. Amer. Math. Soc. 70 (1964), 98-104. MR 28 #1509. MR 158283
- 19.
- G. Lumer, On Wermer's maximality theorem, Invent. Math. 8 (1969), 236-237. MR 40 #4769. MR 251542
- 20.
- D. Sarason, Generalized interpolation in H∞, Trans. Amer. Math. Soc. 127 (1967), 179-203. MR 34 #8193. MR 208383
- 21.
- D. Sarason, An addendum to "Past and future", Math. Scand. 30 (1972), 62-64. MR 385990
- 22.
- D. Sarason, On products of Toeplitz operators, Acta Sci. Math. (Szeged) (to appear). MR 331109
- 22.
- D. Sarason, Invariant subspaces (to appear).
- 24.
- D. Sarason, Approximation of piecewise continuous functions by quotients of bounded analytic functions, Canad. J. Math. 24 (1972), 642-657. MR 310647
- 25.
- W. Scidel, On the distribution of values of bounded analytic functions, Trans. Amer. Math. Soc. 36 (1934), 201-226. MR 1501738
- 27.
- J. Wermer, On algebras of continuous functions, Proc. Amer. Math. Soc. 4 (1953), 866-869. MR 15, 440. MR 58877
- 28.
- L. Zalcman, Bounded analytic functions on domains of infinite connectivity, Trans. Amer. Math. Soc. 144 (1969), 241-269. MR 40 #5884. MR 252665
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (1970):
46J10,
30A76,
30A78
Retrieve articles in all journals
with MSC (1970):
46J10,
30A76,
30A78
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1973-13144-1
PII:
S 0002-9904(1973)13144-1
|
