Holomorphic extensions from open families of circles
Author:
Josip Globevnik
Journal:
Trans. Amer. Math. Soc. 355 (2003), 19211931
MSC (2000):
Primary 30E20
Published electronically:
January 8, 2003
MathSciNet review:
1953532
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Abstract: For a circle write . A continuous function on extends holomorphically from (into the disc bounded by ) if and only if the function defined on has a bounded holomorphic extension into . In the paper we consider open connected families of circles , write , and assume that a continuous function on extends holomorphically from each . We show that this happens if and only if the function defined on has a bounded holomorphic extension into the domain for each open family compactly contained in . This allows us to use known facts from several complex variables. In particular, we use the edge of the wedge theorem to prove a theorem on real analyticity of such functions.
 [AG]
M. Agranovsky and J. Globevnik: Analyticity on circles for rational and realanalytic functions of two real variables. J. d'Analyse Math., to appear.
 [E]
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
 [G1]
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
 [G2]
J. Globevnik: Analyticity on families of curves. Talk at Bar Ilan University, November 1987
 [G3]
Josip
Globevnik, Testing analyticity on rotation
invariant families of curves, Trans. Amer.
Math. Soc. 306 (1988), no. 1, 401–410. MR 927697
(89g:30078), http://dx.doi.org/10.1090/S00029947198809276970
 [G4]
Josip
Globevnik, Holomorphic extensions and rotation invariance,
Complex Variables Theory Appl. 24 (1994), no. 12,
49–51. MR
1269830 (95g:30002)
 [R]
Walter
Rudin, Lectures on the edgeofthewedge theorem, American
Mathematical Society, Providence, R.I., 1971. Conference Board of the
Mathematical Sciences Regional Conference Series in Mathematics, No. 6. MR 0310288
(46 #9389)
 [T]
A. Tumanov: A Morera type theorem in the strip. Preprint.
 [AG]
 M. Agranovsky and J. Globevnik: Analyticity on circles for rational and realanalytic functions of two real variables. J. d'Analyse Math., to appear.
 [E]
 L. Ehrenpreis: Three problems at Mount Holyoke. Radon Transforms and Tomography. Contemp. Math. 278 (2001) 123130. MR 2002d:44002
 [G1]
 J. Globevnik: Analyticity on rotation invariant families of curves. Trans. Amer. Math. Soc. 280 (1983) 247254. MR 85f:30060
 [G2]
 J. Globevnik: Analyticity on families of curves. Talk at Bar Ilan University, November 1987
 [G3]
 J. Globevnik: Testing analyticity on rotation invariant families of curves. Trans. Amer. Math. Soc. 306 (1988) 401410. MR 89g:30078
 [G4]
 J. Globevnik: Holomorphic extensions and rotation invariance. Complex Variables Theory Appl. 24 (1993) 4951. MR 95g:30002
 [R]
 W. Rudin: Lectures on the edge of the wedge theorem. Conf. Ser. in Math. No. 6. American Mathematical Society, Providence, RI, 1971. MR 46:9389
 [T]
 A. Tumanov: A Morera type theorem in the strip. Preprint.
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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/S0002994703032410
PII:
S 00029947(03)032410
Received by editor(s):
July 24, 2002
Published electronically:
January 8, 2003
Dedicated:
Dedicated to Professor Ivan Vidav on the occasion of his eightyfifth birthday
Article copyright:
© Copyright 2003
American Mathematical Society
