Analyticity on translates of a Jordan curve
Author:
Josip Globevnik
Journal:
Trans. Amer. Math. Soc. 359 (2007), 55555565
MSC (2000):
Primary 30E20
Published electronically:
May 8, 2007
MathSciNet review:
2327042
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Abstract: Let be a domain in which is symmetric with respect to the real axis and whose boundary is a real analytic simple closed curve. Translate vertically to get where is such that . We prove that if is a continuous function on such that for each , the function has a continuous extension to which is holomorphic on , then is holomorphic on .
 1.
M. L. Agranovsky: Characterization of CRfunctions by analytic extensions from curves and CRextensions of boundary foliations. To appear in Adv. Math. [ArXiv:math.CV/0511125]
 2.
Mark
L. Agranovsky and Josip
Globevnik, Analyticity on circles for rational and realanalytic
functions of two real variables, J. Anal. Math. 91
(2003), 31–65. MR 2037401
(2004j:30003), http://dx.doi.org/10.1007/BF02788781
 3.
Leon
Ehrenpreis, Three problems at Mount Holyoke, Radon transforms
and tomography (South Hadley, MA, 2000) Contemp. Math., vol. 278,
Amer. Math. Soc., Providence, RI, 2001, pp. 123–130. MR 1851483
(2002d:44002), http://dx.doi.org/10.1090/conm/278/04600
 4.
Josip
Globevnik, Analyticity on rotation invariant
families of curves, Trans. Amer. Math. Soc.
280 (1983), no. 1,
247–254. MR
712259 (85f:30060), http://dx.doi.org/10.1090/S00029947198307122596
 5.
J. Globevnik: Analyticity on familes of curves. Talk at Bar Ilan University, November 1987.
 6.
Josip
Globevnik, Holomorphic extensions from open
families of circles, Trans. Amer. Math.
Soc. 355 (2003), no. 5, 1921–1931 (electronic). MR 1953532
(2003j:30007), http://dx.doi.org/10.1090/S0002994703032410
 7.
Hans
Lewy, On the local character of the solutions of an atypical linear
differential equation in three variables and a related theorem for regular
functions of two complex variables, Ann. of Math. (2)
64 (1956), 514–522. MR 0081952
(18,473b)
 8.
Hugo
Rossi, A generalization of a theorem of Hans
Lewy, Proc. Amer. Math. Soc. 19 (1968), 436–440. MR 0222327
(36 #5379), http://dx.doi.org/10.1090/S00029939196802223270
 9.
A.
Tumanov, A Morera type theorem in the strip, Math. Res. Lett.
11 (2004), no. 1, 23–29. MR 2046196
(2004k:30004), http://dx.doi.org/10.4310/MRL.2004.v11.n1.a3
 10.
A. Tumanov: Testing analyticity on circles. To appear in Amer. J. Math. [ArXiv:math.CV/0502139]
 1.
 M. L. Agranovsky: Characterization of CRfunctions by analytic extensions from curves and CRextensions of boundary foliations. To appear in Adv. Math. [ArXiv:math.CV/0511125]
 2.
 M. L. Agranovsky and J. Globevnik: Analyticity on circles for rational and realanalytic functions of two real variables. J. d'Analyse Math. 91 (2003) 3165. MR 2037401 (2004j:30003)
 3.
 L. Ehrenpreis: Three problems at Mount Holyoke. Contemp. Math. 278 (2001) 123130. MR 1851483 (2002d:44002)
 4.
 J. Globevnik: Analyticity on rotation invariant families of curves. Trans. Amer. Math. Soc. 280 (1983) 247257. MR 712259 (85f:30060)
 5.
 J. Globevnik: Analyticity on familes of curves. Talk at Bar Ilan University, November 1987.
 6.
 J. Globevnik: Holomorphic extensions from open families of circles. Trans. Amer. Math. Soc. 355 (2003) 19211931. MR 1953532 (2003j:30007)
 7.
 H. Lewy: On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables. Ann. of Math. 64 (1956) 514522. MR 0081952 (18:473b)
 8.
 H. Rossi: A generalization of a theorem of Hans Lewy. Proc. Amer. Math. Soc. 19 (1968) 436440. MR 0222327 (36:5379)
 9.
 A. Tumanov: A Morera type theorem in the strip. Math. Res. Lett. 11 (2004) 2329. MR 2046196 (2004k:30004)
 10.
 A. Tumanov: Testing analyticity on circles. To appear in Amer. J. Math. [ArXiv:math.CV/0502139]
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Additional Information
Josip Globevnik
Affiliation:
Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia
Email:
josip.globevnik@fmf.unilj.si
DOI:
http://dx.doi.org/10.1090/S000299470704264X
PII:
S 00029947(07)04264X
Received by editor(s):
June 15, 2005
Received by editor(s) in revised form:
December 1, 2005
Published electronically:
May 8, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
