Fredholm Integral Equations of the Second Kind (Separable Kernel)

Zemyan, Stephen M.

doi:10.1007/978-0-8176-8349-8_1

Stephen M. Zemyan²

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Abstract

In this chapter, our purpose is to examine the Fredholm integral equation of the second kind

$$\phi (x) = f(x) + \lambda \,\int\limits_{a}^{b}K(x,t)\,\phi (t)\,\mathrm{d}t,$$

where K(x, t) is a separable kernel.

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Notes

1.
Separable kernels are also known as degenerate kernels or, in older texts, as Pincherle–Goursat kernels.
2.
In the literature, the adjoint equation is also referred to as the conjugate equation, the transposed equation, or the associated equation.

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

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Stephen M. Zemyan
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Zemyan, S.M. (2012). Fredholm Integral Equations of the Second Kind (Separable Kernel). In: The Classical Theory of Integral Equations. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8349-8_1

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DOI: https://doi.org/10.1007/978-0-8176-8349-8_1
Published: 31 May 2012
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-8348-1
Online ISBN: 978-0-8176-8349-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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