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.
KeywordsSimple layer potential Laplace’s equation Integral equation Integral transforms Solvability of integral equations
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