Skip to main content

Splitting of slowly decreasing ideals in weighted algebras of entire functions

  • Special Year Papers
  • Conference paper
  • First Online:
Book cover Complex Analysis II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1276))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.

    Article  MathSciNet  MATH  Google Scholar 

  2. Berenstein, C. A.; Taylor, B. A.: Interpolation problems in ℂn with applications to harmonic analysis, J. Anal. Math. 38, (1980), 188–254.

    Article  MathSciNet  MATH  Google Scholar 

  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. Beurling, A.: Quasi-analyticity and general distributions, Lectures 4. and 5. AMS Summer Institute, Stanford (1961).

    Google Scholar 

  5. Björck, G.: Linear partial differential operators and generalized distributions, Ark. Mat. 6, (1965), 351–407.

    Article  MathSciNet  MATH  Google Scholar 

  6. Boas, R. P.: Entire Functions, Academic Press (1954).

    Google Scholar 

  7. Cohoon, D. K.: Nonexistence of a continuous right inverse for linear partial differential operators with constant coefficients, Math. Scand. 29, (1971), 337–342.

    MathSciNet  MATH  Google Scholar 

  8. Djakov, P. B.; Mityagin, B. S.: The structure of polynomial ideals in the algebra of entire functions, Stud. Math. 68, (1980), 85–104.

    MathSciNet  MATH  Google Scholar 

  9. Ehrenpreis, L.: Fourier Analysis in Several Complex Variables, New York: Wiley-Interscience Publ. (1976).

    MATH  Google Scholar 

  10. Jarchow, H.: Locally Convex Spaces, Stuttgart: Teubner (1981).

    Book  MATH  Google Scholar 

  11. Kelleher, J. J.; Taylor, B. A.: Closed ideals in locally convex algebras of entire functions, J. Reine Angew. Math. 255, (1972), 190–209.

    MathSciNet  MATH  Google Scholar 

  12. Komatsu, H.: Ultradistributions I, Structure theorems and a characterization, J. Fac. Sci. Tokyo Sec. IA, 20, (1973), 25–105.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  14. Meise, R.: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals, J. Reine Angew. Math. 363, (1985), 59–95.

    MathSciNet  MATH  Google Scholar 

  15. Meise, R.; Taylor, B. A.: Splitting of closed ideals in (DFN)-algebras of entire functions and the property (DN), preprint.

    Google Scholar 

  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. Meise, R.; Schwerdtfeger, K.; Taylor, B. A.: Kernels of slowly decreasing convolution operators, Doga, Tr. J. Math. 10, (1986), 176–197.

    MathSciNet  MATH  Google Scholar 

  18. Meise, R.; Taylor, B. A.; Vogt, D.: Equivalence of slowly decreasing conditions and local Fourier expansions, preprint.

    Google Scholar 

  19. Meise, R.; Vogt, D.: Characterization of convolution operators on spaces of C-functions admitting a continuous linear right inverse, preprint.

    Google Scholar 

  20. Palamodov, V. P.: Linear Differential Operators with Constant Coefficients, Springer 1970.

    Google Scholar 

  21. Rubel, L. A.; Taylor, B. A.: A Fourier series method for meromorphic and entire functions, Bull. Soc. Math. Fr. 96, (1968), 53–96.

    MATH  Google Scholar 

  22. Schwartz, L.: Théorie générale des fonctions moyenne-périodiques, Ann. Math, II. Ser. 48, (1947), 857–929.

    Article  MATH  Google Scholar 

  23. Taylor, B. A.: Linear extension operators for entire functions, Mich. Math. J. 29, (1982), 185–197

    Article  MathSciNet  MATH  Google Scholar 

  24. Treves, F.: Locally Convex Spaces and Linear Partial Differential Equations, Springer (1967).

    Google Scholar 

  25. Vogt, D.: Characterisierung der Unterräume von s, Math. Z. 155, (1977), 109–117.

    Article  MathSciNet  MATH  Google Scholar 

  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. Vogt, D.: On the solvability of P(D)f=g for vector valued functions, RIMS Kokyuroku 508, (1983), 168–182.

    Google Scholar 

  28. Vogt, D.; Wagner, M. J.: Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau, Stud. Math. 67, (1980), 225–240.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Carlos A. Berenstein

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Meise, R., Momm, S., Taylor, B.A. (1987). Splitting of slowly decreasing ideals in weighted algebras of entire functions. In: Berenstein, C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078961

Download citation

  • DOI: https://doi.org/10.1007/BFb0078961

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18357-0

  • Online ISBN: 978-3-540-47904-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics