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Convolution operators with a fundamental solution of finite order

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References

  1. J.Barros-Neto, An introduction to the theory of distributions. New York 1973.

  2. L. Ehrenpreis andP. Malliavin, Invertible operators and interpolation in A U spaces. J. Math. Pures Appl.53, 165–182 (1974).

    Google Scholar 

  3. O. von Grudzinski, Slowly decreasing entire functions and convolution equations. Partial Differential Equations, Banach Cent. Publ.10, 169–184 (1983).

    Google Scholar 

  4. D.Hegen, Existence of a fundamental solution and a definition of hypoellipticity for linear partial differential difference operators with constant coefficients. Master's thesis, Groningen 1992.

  5. L. Hörmander, On the range of convolution operators. Ann. of Math.76, 148–170 (1962).

    Google Scholar 

  6. L.Hörmander, Linear Partial Differential Operators. LNM116, Berlin-Heidelberg-New York 1969.

  7. L.Hörmander, The Analysis of Linear Partial Differential Operators I. Berlin-Heidelberg-New York 1983.

  8. B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution. Ann. Inst. Fourier (Grenoble)6, 271–355 (1955–56).

    Google Scholar 

  9. J. P. Rosay, A very elementary proof of the Malgrange-Ehrenpreis Theorem. Amer. Math. Monthly98, 518–523 (1991).

    Google Scholar 

  10. L.Schwartz, Théorie des distributions. Paris 1966.

  11. H. S. Shapiro, Local solvability of PDE with constant coefficients. Akad. Nauk SSSR170, 314–320 (1989).

    Google Scholar 

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The research was supported by DGICYT under Proyecto PB 91-0538. I would like to thank J. Bonet for interesting conversations and helpful comments on the topic of this paper.

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Galbis, A. Convolution operators with a fundamental solution of finite order. Arch. Math 65, 263–266 (1995). https://doi.org/10.1007/BF01195097

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