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Estimations for the Solutions of Operator Linear Differential Equations

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Generalized Functions, Convergence Structures, and Their Applications

Abstract

In this paper we observe the approximate solution of the linear operator differential equation and estimate the error of approximation. For this purpose we use the results from [6]. They enable us to introduce some measures of approximation on the space L of locally integrable functions on [0,∞) and on the field of Mikusiński operators.

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References

  1. T. Boehme, The Mikusiński Operator as a Topological Space, Amer. J. Math., 98, 55–66 (1976).

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  2. J. Burzyk, On Convergence in the Mikusiński Operational Calculus, Stud. Math., 75, 313–333 (1983).

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  3. J. Burzyk and P. Mikusiński, On normability of semigroups, Bull. Acad. Polon. Sci., Ser. Math. Astronom. Phys., 1–2, 33–35 (1980).

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  4. A. A. Lokšin, V. E. Rok, Automodal solution of the wave equation with delayed time, Uspehi Mat. Nauk., T. 33. N°. 6 (204), 221–222, (1980), (in Russian).

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  5. J. Mikusiński, “Operational calculus”, Pergamon Press, Warszawa (1959).

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  6. E. Pap and Đ. Takači, Convergences of the solutions of operator linear differential equations (to appear).

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  7. B. Stanković, Approximate solution of the operator linear differential equation I, Publ. de l’Inst. Math., T. 21(35), 185–196 (1977).

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Novi Sad, dr I. Đuričića 4, 21000, Novi Sad, Yugoslavia

    Endre Pap & Đurđica Takači

Authors
  1. Endre Pap
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  2. Đurđica Takači
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Novi Sad, Yugoslavia

    Bogoljub Stanković , Endre Pap  & Stevan Pilipović ,  & 

  2. Steklov Institute of Mathematics, Moscow, USSR

    Vasilij S. Vladimirov

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© 1988 Plenum Press, New York

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Pap, E., Takači, Đ. (1988). Estimations for the Solutions of Operator Linear Differential Equations. In: Stanković, B., Pap, E., Pilipović, S., Vladimirov, V.S. (eds) Generalized Functions, Convergence Structures, and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1055-6_27

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  • DOI: https://doi.org/10.1007/978-1-4613-1055-6_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8312-6

  • Online ISBN: 978-1-4613-1055-6

  • eBook Packages: Springer Book Archive

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