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A Mikusinski calculus for the bessel operator Bμ

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Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 564))

Abstract

An operational calculus for the Bessel operator Bμ=t-μDtμ+1D(−1<μ<∞) is developed. A convolution process is proposed which reduces to Ditkin's convolution when μ=0. Following Mikusinski, the construction is through the field extension of a commutative ring without zero divisors. The relationships between the calculus and those of Mikusinski and Ditkin are shown.

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References

  1. Koh, E. L., T. H. Darmstadt, preprint No. 240, 1975.

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  2. Ditkin, V. A. and A. P. Prudnikov, Integral Transforms and Operational Calculus, Pergamon, 1965.

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  3. Meller, N. A., Vichis. Matem. 6 (1960) 161–168.

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  4. Mikusinski, J., Operational Calculus, Pergamon, 1959.

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  5. Ross, B. (Ed.) Fractional Calculus and its Applications, Springer-Verlag, 1975.

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  6. Dimovski, I. H., Compt. Rend. Acad. Bulg. Sci. 26 (1973) 1579–1582.

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  7. Mikusinski, J. and C. R. Nardzewski, Studia Math. 13 (1) (1953) 62–68.

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  8. Erdélyi, A. et al. Higher Transcendental Functions, Vol. 2, McGraw-Hill, 1954.

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Authors
  1. Eusebio L. Koh
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Editor information

William N. Everitt Brian D. Sleeman

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© 1976 Springer-Verlag

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Koh, E.L. (1976). A Mikusinski calculus for the bessel operator Bμ . In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087345

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  • DOI: https://doi.org/10.1007/BFb0087345

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08058-9

  • Online ISBN: 978-3-540-37517-3

  • eBook Packages: Springer Book Archive

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