Abstract
In this chapter, we provide well-known mathematical facts that we rely upon in the following discussion. We give elements of the potential theory for Laplace’s equation and then formulate the most important theorems of solvability of integral equations. This is followed by consideration of integral transforms, which are the most useful in geophysical problems. More detailed exposition of the material in this chapter can be found in the cited literature on integral equations, equations of mathematical physics, and functional analysis.
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References
B.K. Driver, Compact and Fredholm operators and the spectral theorem. In Analysis Tools with Applications, Chapter 35 (Springer, Berlin, 2003), pp. 579–600
N.M. Gunther, La théorie Du Potentiel et Ses Applications Aux problèmes Fondamentaux de la Physique Mathématique (Gauthier-Villars, Paris, 1934)
I.G. Petrovskii, Lekcii po teorii integral’nykh uravneniy (Nauka, Moscow, 1965)
A.N. Tikhonov, A.A. Samarskii, Equations of Mathematical Physics. (Translation from Russian) (Pergamon, 1963)
F.G. Tricomi, Integral Equations (Interscience, New York, 1957)
V.S. Vladimirov, Equations of Mathematical Physics (Marcel Dekker, New York, 1971)
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Mukanova, B., Modin, I. (2018). Mathematical Background. In: The Boundary Element Method in Geophysical Survey. Innovation and Discovery in Russian Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-72908-4_2
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DOI: https://doi.org/10.1007/978-3-319-72908-4_2
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