Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Holomorphic approximation to boundary value algebras

Author(s): Frank T. Birtel
Journal: Bull. Amer. Math. Soc. 84 (1978), 406-416.
MSC (1970): Primary 32E25, 32E30; Secondary 32D10, 32D15, 32F15, 46J10
MathSciNet review: 0460719
Retrieve article in: PDF

References | Similar articles | Additional information

References:

1.
R. Arens, The maximal ideals of certain function algebras, Pacific J. Math. 8 (1958), 641-648. MR 22 #8315. MR 117537
2.
F. Beatrous, Boundary value algebras, Dissertation, Tulane Univ., 1978.
3.
E. Bedford and J. E. Fornaess, Domains with pseudoconvex neighborhood systems (to appear). MR 499316
4.
F. T. Birtel, Algebras of holomorphic functions, Tulane Lecture Note Series, 1972, pp. 1-100.
5.
F. T. Birtel, Mergelyan approximation on holomorphic sets, Bull. Inst. Math. Acad. Sinica 3 (1975), 183-190. MR 447630
6.
F. T. Birtel, Some holomorphic function algebras, Papers from the Summer Gathering on Function Algebras, Matematisk Inst., Aarhus Univ., Aarhus, 1969, pp. 11-18. MR 254598
7.
E. M. Cirka, Approximation by holomorphic functions on smooth manifolds in C, Mat. Sb. 78 (1969), 101-123 = Math. USSR-Sb. 7 (1969), 95-113. MR 239121
8.
B. Cole and R. M. Range, A-measures on complex manifolds and some applications, J. Functional Analysis 11 (1972), 393-400. MR 340646
9.
K. Diederich and J. E. Fornaess, Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), 129-141. MR 437806
10.
K. Diederich and J. E. Fornaess, Pseudoconvex domains: An example with nontrivial Nebenhülle, Math. Ann. 225 (1947), 275-292. MR 430315
11.
K. Diederich and J. E. Fornaess, Pseudoconvex domains: Existence of stein neighborhoods, Duke Math. J. 44 (1977), 641-662. MR 447634
12.
K. Diederich and J. E. Fornaess, A strange bounded smooth domain of holomorphy, Bull. Amer. Math. Soc. 82 (1976), 74-76. MR 397019
13.
K. Diederich and J. E. Fornaess, Pseudoconvex domains with real-analytic boundary (to appear). MR 477153
14.
H. Federer, Geometric measure theory. Springer-Verlag, New York, 1969. MR 257325
15.
J. E. Fornaess, Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math. 98 (1976), 529-569. MR 422683
16.
J. E. Fornaess and A. Nagel, The Mergelyan property for weakly pseudoconvex domains, Manuscripta Math. 22 (1977), 199-208. MR 457779
17.
T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. MR 410387
18.
M. Hakim and N. Sibony, Frontière de Shilov et spectre de $A(\bar D)$ pour les domains failblement pseudoconvexes, C. R. Acad. Sci., Paris 281 (1975), 959-962. MR 390287
19.
F. R. Harvey and H. B. Lawson, Boundaries of complex varieties. I, Ann. of Math. (2) 102 (1975), 223-290. MR 425173
20.
G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Mat. Sb. 78 (120) (1969), 611-632 = Math. USSR Sb. 7 (1969), 597-616. MR 249660
21.
G. M. Henkin and E. M. Cirka, Boundary properties of holomorphic functions of several complex variables, J. Soviet Math. 5 (1976), 612-679. MR 477155
22.
L. Hörmander and J. Wermer, Uniform approximation on compact sets in C, Math. Scand. 23 (1968), 5-21. MR 254275
23.
E. Kallin, Fat polynomially convex sets, Function Algebras, Scott, Foresman, Chicago, 111., 1966, pp. 149-152. MR 33 #2828. MR 194618
24.
N. Kerzman, Hölder and L, Comm. Pure Appl. Math. 24 (1971), 301-379. MR 43 #7658. MR 281944
25.
I. Lieb, Ein Approximationssatz auf streng pseudokonvexen Gebieten, Math. Ann. 184 (1969), 56-60. MR 262540
26.
R. M. Range and Y. T. Siu, Uniform estimates for the $\bar \partial $-equation on domains with smooth strictly pseudoconvex boundaries, Math. Ann. 206 (1973), 325-354. MR 338450
27.
V. N. Senichkin, On the approximation of functions of several complex variables on fat compact subsets of C, Mat. Sb. 97 (139) (1975), no. 2, 278-300 = Math. USSR Sb. 26 (1975), 260-279. MR 397017
28.
N. Sibony, Approximation de fonctions à valeurs dans un Fréchet, par des functions holomorphes, Ann. Inst. Fourier (Grenoble) 24 (1974), 167-179. MR 51 #934. MR 364680
29.
N. Sibony, Multidimensional analytic structure in the spectrum of a uniform algebra, Lecture Notes in Math., no. 512, Springer-Verlag, New York, 1976 (also appeared in Spaces of analytic functions, Kristiansand, Norway, 1975). MR 632106
30.
N. Sibony, Un example de compact polynomialement convexe dans C2, Bull. Soc. Math. France 103 (1975), 141-147. MR 387659
31.
N. Sibony and J. Wermer, Generators for A (Ω), Trans. Amer. Math. Soc. 194 (1924), 103-114. MR 419838
32.
A. G. Vitushkin, Analytic capacity of sets in problems of approximation theory, Russian Math. Surveys 22 (1967), 139-201. MR 37 #5404. MR 229838
33.
B. Weinstock, Approximation by holomorphic functions on certain product sets in Cn, Pacific J. Math. 43 (1972), 811-822. MR 344523
34.
B. Weinstock, Some conditions for uniform H-convexity, Illinois J. Math. 19 (1975), 400-404. MR 53 #13639. MR 409887
35.
R. M. Range, Holomorphic approximation near strictly pseudoconvex boundary points, Math. Ann. 201 (1973), 9-17. MR 324074

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 32E25, 32E30, 32D10, 32D15, 32F15, 46J10

Retrieve articles in all Journals with MSC (1970): 32E25, 32E30, 32D10, 32D15, 32F15, 46J10


Additional Information:

DOI: 10.1090/S0002-9904-1978-14480-2
PII: S 0002-9904(1978)14480-2




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia