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A Cauchy Integral Equation Method for Half-Space Convolution Equations

  • Chapter
Modern Mathematical Methods in Transport Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 51))

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Abstract

A method for solving in closed analytical form half-space convolution equations is described here. By an inverse Laplace transformation the convolution equation is transformed into a Cauchy type singular integral equation. Six different examples, taken from radiative transfer and the kinetic theory of gases, are presented to illustrate the method and the need to sometimes introduce distributional solutions, which, for transport problems, correspond to the real discrete eigenvalues of the spectrum.

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Author information

Authors and Affiliations

  1. CNRS, Observatoire de la Côte d’Azur, B. P. 139, F-06003, Nice-cedex, France

    H. Frisch

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  1. H. Frisch
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, Virginia, 24061, USA

    William Greenberg

  2. Dept. of Chemistry and Dept. of Applied Mathematics, SUNY, Stony Brook, New York, 11794, USA

    Jacek Polewczak

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© 1991 Springer Basel AG

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Frisch, H. (1991). A Cauchy Integral Equation Method for Half-Space Convolution Equations. In: Greenberg, W., Polewczak, J. (eds) Modern Mathematical Methods in Transport Theory. Operator Theory: Advances and Applications, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5675-1_11

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  • DOI: https://doi.org/10.1007/978-3-0348-5675-1_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5677-5

  • Online ISBN: 978-3-0348-5675-1

  • eBook Packages: Springer Book Archive

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