Splitting of slowly decreasing ideals in weighted algebras of entire functions

  • Reinhold Meise
  • Siegfried Momm
  • B. Alan Taylor
Special Year Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1276)


Weight Function Exact Sequence Entire Function Quotient Space Convolution Operator 
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  1. [1]
    Berenstein, C. A.; Taylor, B. A.: A new look at interpolation theory for entire functions of one variable, Adv. Math. 33, (1979), 109–143.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Berenstein, C. A.; Taylor, B. A.: Interpolation problems in ℂn with applications to harmonic analysis, J. Anal. Math. 38, (1980), 188–254.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Berenstein, C. A.; Taylor, B. A.: On the geometry of interpolating varieties, pp. 1–25 in Seminaire Lelong-Skoda, Springer LNM 919 (1982).Google Scholar
  4. [4]
    Beurling, A.: Quasi-analyticity and general distributions, Lectures 4. and 5. AMS Summer Institute, Stanford (1961).Google Scholar
  5. [5]
    Björck, G.: Linear partial differential operators and generalized distributions, Ark. Mat. 6, (1965), 351–407.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Boas, R. P.: Entire Functions, Academic Press (1954).Google Scholar
  7. [7]
    Cohoon, D. K.: Nonexistence of a continuous right inverse for linear partial differential operators with constant coefficients, Math. Scand. 29, (1971), 337–342.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Djakov, P. B.; Mityagin, B. S.: The structure of polynomial ideals in the algebra of entire functions, Stud. Math. 68, (1980), 85–104.MathSciNetzbMATHGoogle Scholar
  9. [9]
    Ehrenpreis, L.: Fourier Analysis in Several Complex Variables, New York: Wiley-Interscience Publ. (1976).zbMATHGoogle Scholar
  10. [10]
    Jarchow, H.: Locally Convex Spaces, Stuttgart: Teubner (1981).CrossRefzbMATHGoogle Scholar
  11. [11]
    Kelleher, J. J.; Taylor, B. A.: Closed ideals in locally convex algebras of entire functions, J. Reine Angew. Math. 255, (1972), 190–209.MathSciNetzbMATHGoogle Scholar
  12. [12]
    Komatsu, H.: Ultradistributions I, Structure theorems and a characterization, J. Fac. Sci. Tokyo Sec. IA, 20, (1973), 25–105.MathSciNetzbMATHGoogle Scholar
  13. [13]
    Malgrange, B.: Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble) 6, (1955/56), 271–355.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Meise, R.: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals, J. Reine Angew. Math. 363, (1985), 59–95.MathSciNetzbMATHGoogle Scholar
  15. [15]
    Meise, R.; Taylor, B. A.: Splitting of closed ideals in (DFN)-algebras of entire functions and the property (DN), preprint.Google Scholar
  16. [16]
    Meise, R.; Taylor, B. A.: Each non-zero convolution operator on the entire functions admits a continuous linear right inverse, preprint.Google Scholar
  17. [17]
    Meise, R.; Schwerdtfeger, K.; Taylor, B. A.: Kernels of slowly decreasing convolution operators, Doga, Tr. J. Math. 10, (1986), 176–197.MathSciNetzbMATHGoogle Scholar
  18. [18]
    Meise, R.; Taylor, B. A.; Vogt, D.: Equivalence of slowly decreasing conditions and local Fourier expansions, preprint.Google Scholar
  19. [19]
    Meise, R.; Vogt, D.: Characterization of convolution operators on spaces of C-functions admitting a continuous linear right inverse, preprint.Google Scholar
  20. [20]
    Palamodov, V. P.: Linear Differential Operators with Constant Coefficients, Springer 1970.Google Scholar
  21. [21]
    Rubel, L. A.; Taylor, B. A.: A Fourier series method for meromorphic and entire functions, Bull. Soc. Math. Fr. 96, (1968), 53–96.zbMATHGoogle Scholar
  22. [22]
    Schwartz, L.: Théorie générale des fonctions moyenne-périodiques, Ann. Math, II. Ser. 48, (1947), 857–929.CrossRefzbMATHGoogle Scholar
  23. [23]
    Taylor, B. A.: Linear extension operators for entire functions, Mich. Math. J. 29, (1982), 185–197MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Treves, F.: Locally Convex Spaces and Linear Partial Differential Equations, Springer (1967).Google Scholar
  25. [25]
    Vogt, D.: Characterisierung der Unterräume von s, Math. Z. 155, (1977), 109–117.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Vogt, D.: Subspaces and quotient spaces of (s), pp. 167–187 "Functional Analysis: Surveys and Recent Results", K.-D. Bierstedt, B. Fuchssteiner (Eds.), North-Holland Mathematics Studies 27, (1977).Google Scholar
  27. [27]
    Vogt, D.: On the solvability of P(D)f=g for vector valued functions, RIMS Kokyuroku 508, (1983), 168–182.Google Scholar
  28. [28]
    Vogt, D.; Wagner, M. J.: Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau, Stud. Math. 67, (1980), 225–240.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Reinhold Meise
    • 1
    • 2
  • Siegfried Momm
    • 1
    • 2
  • B. Alan Taylor
    • 1
    • 2
  1. 1.Mathematisches Institut der UniversitätDüsseldorf 1Federal Republic of Germany
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUnited States of America

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