Integral Equations of the Second Kind with a Symmetric Kernel

Sudeshna Banerjea and Birendra Nath Mandal
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Sudeshna Banerjea: Jadavpur University, Department of Mathematics
Birendra Nath Mandal: Indian Statistical Institute, Physics and Applied Mathematics Unit

Chapter Chapter 4 in Integral Equations and Integral Transforms, 2023, pp 81-96 from Springer

Abstract: Abstract The Fredholm integral equation of the second kind given by $$\phi (x)=f(x)+\lambda \int _{a}^{b} k(x,t) \phi (t)~ dt,~~~a\le x\le b$$ may be expressed in the operator form as $$(I-\lambda K)\phi =f,$$ where $$(K \phi )(x)=\int _{a}^{b}k(x,t)\phi (t)~dt.$$ In this chapter, the method of the solution of integral equation (4.1) is discussed when its kernel k(x, t) is symmetric.

Date: 2023
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DOI: 10.1007/978-981-99-6360-7_4

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