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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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Analytic functionals with unbounded carriers and mean periodic functions
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by Alex Meril PDF
Trans. Amer. Math. Soc. 278 (1983), 115-136 Request permission

Abstract:

We study certain ideals in some spaces of analytic functionals with unbounded carriers introduced by T. Kawaï, M. Morimoto and J. W. de Roever. Using Banach algebra methods, we show an example of space without spectral synthesis. Using Hörmander’s ${L^2}$ estimates, we prove a spectral synthesis theorem for mean periodic functions.
References
    E. Amar, $\bar \partial$ cohomologie ${C^\infty }$ et applications, Prep. Univ. Paris Sud 80 T. 1.
  • Carlos A. Berenstein and B. A. Taylor, A new look at interpolation theory for entire functions of one variable, Adv. in Math. 33 (1979), no. 2, 109–143. MR 544846, DOI 10.1016/S0001-8708(79)80002-X
  • Leon Ehrenpreis, Appendix to the paper “Mean periodic functions I”, Amer. J. Math. 77 (1955), 731–733. MR 76303, DOI 10.2307/2372594
    • R. Gay, Division des fonctionelles analytiques et fonctions entières de type exponentiel de plusieurs variables, Th. Sc. Math., Strasbourg, 1976.
  • Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
  • 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
    • —, An introduction to complex analysis in several variables, 2nd ed., North-Holland, Amsterdam, 1973.
  • Takahiro Kawai, On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo Sect. I A Math. 17 (1970), 467–517. MR 0298200
  • Hikosaburo Komatsu, Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan 19 (1967), 366–383. MR 217557, DOI 10.2969/jmsj/01930366
  • Gottfried Köthe, Topological vector spaces. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 237, Springer-Verlag, New York-Berlin, 1979. MR 551623
  • Pierre Lelong, Fonctionnelles analytiques et fonctions entières ($n$ variables), Séminaire de Mathématiques Supérieures, No. 13 (Été, vol. 1967, Les Presses de l’Université de Montréal, Montreal, Que., 1968 (French). MR 0466606
  • Bernard Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble) 6 (1955/56), 271–355 (French). MR 86990
  • Mitsuo Morimoto, Analytic functionals with non-compact carrier, Tokyo J. Math. 1 (1978), no. 1, 77–103. MR 502814, DOI 10.3836/tjm/1270216594
    • J. W. de Roever, Fourier transform of holomorphic functions and application to Newton interpolation series. I, Publ. Math. Centrum, Amsterdam, 1974. —, Fourier transform of holomorphic functions and application to Newton interpolation series. II, T. W 148, Math. Centrum, Amsterdam, 1975.
  • J. W. de Roever, Complex Fourier transformation and analytic functionals with unbounded carriers, Mathematical Centre Tracts, vol. 89, Mathematisch Centrum, Amsterdam, 1978. With a preface by E. M. de Jager. MR 494067
  • Yutaka Saburi, Vanishing theorems of cohomology groups with coefficients in sheaves of holomorphic functions with bounds, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), no. 9, 274–278. MR 517669
  • Laurent Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. (2) 48 (1947), 857–929 (French). MR 23948, DOI 10.2307/1969386
  • François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
    • V. V. Zarinov, Laplace transformation of Fourier hyperfunctions and related classes of analytic functionals. I, Theoret. and Math. Phys. 33 (1978), 1027-1039. —, Laplace transformation of Fourier hyperfunctions and related classes of analytic functionals. II, Theoret. and Math. Phys. 37 (1979), 843-855.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 278 (1983), 115-136
  • MSC: Primary 46F15; Secondary 30H05, 32A07, 32A10
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0697064-1
  • MathSciNet review: 697064