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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Holomorphic extension and decomposition from a totally real manifold
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by Zai Fei Ye PDF
Trans. Amer. Math. Soc. 339 (1993), 1-33 Request permission

Abstract:

This paper is to develop an elementary cohomological approach for decomposing a function into boundary values of holomorphic functions and for discussing the corresponding microlocal analysis and hyperfunction theory.
References
    H. Alexander, Personal communication to Rosay and Stout.
  • É. Amar, On the extension of C.R. functions, Math. Z. 206 (1991), no. 1, 89–102. MR 1086816, DOI 10.1007/BF02571328
  • A. Andreotti and D. C. Hill, E. E. Levi convexity and the Hans Lewy problem. I, II, Ann. Scuola Norm. Sup. Pisa 26 (1972), 325-363, 747-806.
  • M. S. Baouendi, C. H. Chang, and F. Trèves, Microlocal hypo-analyticity and extension of CR functions, J. Differential Geom. 18 (1983), no. 3, 331–391. MR 723811
  • M. S. Baouendi and Linda Preiss Rothschild, Normal forms for generic manifolds and holomorphic extension of CR functions, J. Differential Geom. 25 (1987), no. 3, 431–467. MR 882830
  • M. S. Baouendi and Linda Preiss Rothschild, Extension of holomorphic functions in generic wedges and their wave front sets, Comm. Partial Differential Equations 13 (1988), no. 11, 1441–1466. MR 956829, DOI 10.1080/03605308808820583
  • M. S. Baouendi, Linda Preiss Rothschild, and F. Trèves, CR structures with group action and extendability of CR functions, Invent. Math. 82 (1985), no. 2, 359–396. MR 809720, DOI 10.1007/BF01388808
  • M. S. Baouendi and F. Trèves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math. (2) 113 (1981), no. 2, 387–421. MR 607899, DOI 10.2307/2006990
  • W. Calbeck, Ph.D. thesis, Univ. of Wisconsin-Madison, 1990.
  • Pierre Dolbeault, Formes différentielles et cohomologie sur une variété analytique complexe. I, Ann. of Math. (2) 64 (1956), 83–130 (French). MR 83166, DOI 10.2307/1969950
  • Alain Dufresnoy, Sur l’opérateur $d^{\prime \prime }$ et les fonctions différentiables au sens de Whitney, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 1, xvi, 229–238 (French, with English summary). MR 526786
  • Reese Harvey, The theory of hyperfunctions on totally real subsets of a complex manifold with applications to extension problems, Amer. J. Math. 91 (1969), 853–873. MR 257400, DOI 10.2307/2373307
  • —, Integral formulae connected by Dolbeault’s isomorphism, Rice Univ. Stud. 51 (1970), 77-97.
  • Reese Harvey and John Polking, Fundamental solutions in complex analysis. I. The Cauchy-Riemann operator, Duke Math. J. 46 (1979), no. 2, 253–300. MR 534054
  • F. Reese Harvey and R. O. Wells Jr., Holomorphic approximation and hyperfunction theory on a $C^{1}$ totally real submanifold of a complex manifold, Math. Ann. 197 (1972), 287–318. MR 310278, DOI 10.1007/BF01428202
  • G. M. Henkin and J. Leiterer, Theory of functions on complex manifolds, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], vol. 60, Akademie-Verlag, Berlin, 1984. MR 795028
  • Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
  • Lars Hörmander, $L^{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152. MR 179443, DOI 10.1007/BF02391775
  • André Martineau, Le “edge of the wedge theorem” en théorie des hyperfonctions de Sato, Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969) Univ. Tokyo Press, Tokyo, 1970, pp. 95–106 (French). MR 0267128
  • André Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math. 11 (1963), 1–164 (French). MR 159220, DOI 10.1007/BF02789982
  • A. Martineau, Distributions et valeurs au bord des fonctions holomorphes, Theory of Distributions (Proc. Internat. Summer Inst., Lisbon, 1964), Inst. Gulbenkian Ci., Lisbon, 1964, pp. 193–326 (French). MR 0219754
  • S. Pinčuk, Bogoliubov’s theorem on the "edge of the wedge" for generic manifolds, Math. USSR-Sb. 23 (1974), 441-455.
  • R. Michael Range and Yum-Tong Siu, Uniform estimates for the $\bar \partial$-equation on domains with piecewise smooth strictly pseudoconvex boundaries, Math. Ann. 206 (1973), 325–354. MR 338450, DOI 10.1007/BF01355986
  • Jean-Pierre Rosay, À propos de “wedges” et d’“edges”, et de prolongements holomorphes, Trans. Amer. Math. Soc. 297 (1986), no. 1, 63–72 (French, with English summary). MR 849467, DOI 10.1090/S0002-9947-1986-0849467-2
  • J.-P. Rosay and E. L. Stout, Rado’s theorem for $CR$-functions, preprint.
  • Walter Rudin, Lectures on the edge-of-the-wedge theorem, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 6, American Mathematical Society, Providence, R.I., 1971. MR 0310288
  • Mikio Sato, Theory of hyperfunctions. I, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1959), 139–193. MR 114124
  • Mikio Sato, Takahiro Kawai, and Masaki Kashiwara, Microfunctions and pseudo-differential equations, Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau), Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973, pp. 265–529. MR 0420735
  • P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., vol. 126, Springer-Verlag, Berlin and New York, 1970.
  • Jean-Pierre Serre, Un théorème de dualité, Comment. Math. Helv. 29 (1955), 9–26 (French). MR 67489, DOI 10.1007/BF02564268
  • F. Trèves, Approximation and representation of functions and distributions annihilated by a system of complex vector fields, École Polytechnique, Centre de Mathématiques, Palaiseau, 1981. MR 716137
  • Yoshimichi Tsuno, Integral representation of an analytic functional, J. Math. Soc. Japan 34 (1982), no. 3, 379–391. MR 659610, DOI 10.2969/jmsj/03430379
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 1-33
  • MSC: Primary 32D15; Secondary 32A40, 32F25
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1123459-4
  • MathSciNet review: 1123459