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Generalized Functions, Convergence Structures, and Their Applications pp 267–277Cite as

Estimations for the Solutions of Operator Linear Differential Equations

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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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