Fredholm Integral Equations of the Second Kind (General Kernel)

Stephen M. Zemyan
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Stephen M. Zemyan: Pennsylvania State University Mont Alto, Department of Mathematics

Chapter Chapter 2 in The Classical Theory of Integral Equations, 2012, pp 31-84 from Springer

Abstract: Abstract In Chap. 1, we conducted a thorough examination of the Fredholm integral equation of the second kind for an arbitrary complex parameter λ, assuming that the free term f(x) is complex-valued and continuous on the interval [a, b] and that the kernel K(x, t) is complex-valued, continuous, and separable on the square Q(a, b) = { (x, t): [a, b] ×[a, b]}. We stated the four Fredholm theorems and the Fredholm Alternative Theorem which provide for the construction of all possible solutions to the equation under these assumptions.

Keywords: Integral Equation; Meromorphic Function; Fredholm Integral Equation; Free Term; Closed Disk (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8349-8_2

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DOI: 10.1007/978-0-8176-8349-8_2

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