# Questions tagged [integral-equations]

This tag is about questions regarding the integral equations. An integral equation is an equation in which the unknown function appears under the integral sign. There is no universal method for solving integral equations. Solution methods and even the existence of a solution depend on the particular form of the integral equation.

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### Fredholm integral equation, exercise 12 Functional analysis Kreyszig

I'm trying to do a exercise of Kreyszig book of functional analysis but I'm stuck, I'm trying to solve the integral equation \begin{equation} x(s)-\mu \int_{0}^{2\pi}sin(s)cos(t)x(t)dt =\hat{y}(s) \...
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### An analytical solution of the integral equation $\int_0^\rho \left( \frac{s}{\rho} \right)^3 f(s) \, \mathrm{d}s +\int_\rho^1 f(s)\,\mathrm{d}s=1$

While elaborating on the solution for the Green's function of a mechanics problem involving disks moving on an interface, I came across the following integral equation for the unknown function $f(s)$: ...
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### How to determine two functions from an equation relating their Fourier series coefficients

I'm trying to solve a boundary value problem (Laplace's equation within a rectangle), with a peculiar combination of boundary conditions: one side of the rectangle has a homogeneous Dirichlet boundary ...
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### Solving acausal power-law convolution on a finite interval

I'm trying to solve the following integral equation for x(t): $$\int_0^1 x(\tau) \ G(\tau - t) \ d\tau = y(t)$$ with acausal $G$ defined for the entire real line: $$G(t) = |t|^{-a}$$ Some $y$ of ...
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### Does the Riemann-Lebesgue Lemma Apply to $L^1$ or $L^2$ Space?

In the literature on inverse problems, the Riemann-Lebesgue lemma is often used to demonstrate the ill-posedness of integral equations with square-integrable kernels. For example, in Groetsch (1984), ...
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