Abstract
It is an object of this Chapter to remove some of the mystique associated with generalized functions and to advocate their use in the analysis of physical problems. We will define their properties without proof and direct those interested in pursuing the fundamentals of generalized functions to Lighthill (1958), Gelfand & Shilov (1964) and Jones (1966) who give comprehensive accounts of the general theory with proofs of properties. We lean heavily on these works in recognizing that generalized functions can essentially be manipulated according to the usual rules of addition, differentiation and integration, though in general they may not be multiplied by other than ordinary functions. They provide a powerful extension of the normal mathematical equipment available to physicists.
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Referencess
Lighthill, M.J. (1958) Fourier Analysis and Generalised Functions. Cambridge University Press.
Gelfand, I.M. & Shilov, G.E. (1964) Generalised Functions. Academic Press.
Jones, D.S. (1966) Generalised Functions. McGraw-Hill.
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© 1992 Springer-Verlag Berlin Heidelberg
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Crighton, D.G., Dowling, A.P., Williams, J.E.F., Heckl, M., Leppington, F.G. (1992). Generalized Functions. In: Modern Methods in Analytical Acoustics. Springer, London. https://doi.org/10.1007/978-1-4471-0399-8_2
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DOI: https://doi.org/10.1007/978-1-4471-0399-8_2
Publisher Name: Springer, London
Print ISBN: 978-3-540-19737-9
Online ISBN: 978-1-4471-0399-8
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