|
Quasi-analytic vectors and quasi-analytic functions
Author(s):
Paul R.
Chernoff
Journal:
Bull. Amer. Math. Soc.
81
(1975),
637-646.
MSC (1970):
Primary 26A93, 30A78, 47B25, 47D05
MathSciNet review:
0636276
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- S. Bochner and A. E. Taylor, Some theorems on quasi-analyticity for functions of several variables, Amer. J. Math. 61 (1939), 303-329. MR 1507378
- 2.
- T. Carleman, Les fonctions quasi-analytiques Gauthier-Villars, Paris, 1926.
- 3.
- P. R. Chernoff, Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc. 167 (1972), 105-113. MR 45 #4193. MR 295125
- 4.
- L. Ehrenpreis, Fourier analysis in several complex variables, Pure and Appl. Math., vol. 17, Wiley, New York, 1970. MR 44 #3066. MR 285849
- 5.
- A. Gorny, Contribution à l'étude des fonctions dérivables d'une variable réelle, Acta Math. 71 (1939), 317-358. MR 1, 137; 400. MR 848
- 6.
- W. Groening, Analytic functions with quasi-analytic boundary values, Trans. Amer. Math. Soc. 143 (1969), 95-107. MR 412426
- 7.
- W. Groening, Quasi-analyticity for functions of several variables, Duke Math. J. 38 (1971), 109-115. MR 42 #7933. MR 273052
- 8.
- M. Hasegawa, On quasi-analytic vectors for dissipative operators, Proc. Amer. Math. Soc. 29 (1971), 81-84. MR 43 #981. MR 275224
- 9.
- E. Hille and R. S. Phillips, Functional analysis and semi-groups, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R.I., 1957. MR 19, 664. MR 89373
- 10.
- V. G. Hryptun, Classes of functions quasianalytic with respect to an ordinary linear differential operator, and their applications, Dokl. Akad. Nauk SSSR 177 (1967), 528-530=Soviet Math. Dokl. 8 (1967), 1456-1459. MR 37 #2927. MR 227342
- 11.
- A. N. Kolmogorov, On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Učen. Zap. Moskov. Gos. Univ. Mat. 30 (1939), 3-13 ; English transl., Amer. Math. Soc. Transl. (1) 2 (1962), 233-243. MR 1, 298.
- 12.
- B. I. Korenbljum, Conditions of nontriviality of certain classes of functions analytic in a sector, and problems of quasianalyticity, Dokl. Akad. Nauk. SSSR 166 (1966), 1046-1049=Soviet Math. Dokl. 7 (1966), 232-236. MR 34 #1528. MR 201646
- 13.
- S. Mandelbrojt, Séries adherentes, régularisation des suites, applications, Gauthier Villars, Paris, 1952. MR 14, 542. MR 51893
- 14.
- D. Masson and W. McClary, Classes of C, J. Functional Analysis 10 (1972), 19-32. MR 372673
- 15.
- E. Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572-615. MR 21 #5901. MR 107176
- 16.
- A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191. MR 33 #3105. MR 194899
- 17.
- A. E. Nussbaum, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305-309. MR 40 #4781. MR 251554
- 18.
- W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1966. MR 35 #1420. MR 210528
- 19.
- B. Simon, The theory of semi-analytic vectors: A new proof of a theorem of Masson and McClary, Indiana Univ. Math. J. 20 (1970/71), 1145-1151. MR 44 #7357. MR 290173
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1970):
26A93, 30A78, 47B25, 47D05
Retrieve articles in all Journals with MSC
(1970):
26A93, 30A78, 47B25, 47D05
Additional Information:
DOI:
10.1090/S0002-9904-1975-13806-7
PII:
S 0002-9904(1975)13806-7
|
