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MathematicalPhysicist

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I need to find the Fourier transform of f(x) which is given by the equation:

[tex]-\frac{d^2f(x)}{dx^2}+\frac{1}{a^3}\int_{-\infty}^{\infty}dx'exp(-\lambda|x-x'|)f(x')=\frac{b}{a^2}exp(-\lambda|x|)[/tex]

ofcourse Iv'e taken the Fourier tarnsform of both sides, but I don't see how to calcualte the Fourier tranform of the integral in the above equation, I feel I need to use the definition of dirac's delta function, but don't see how to do this, any ideas, hints?

thanks in advance.

[tex]-\frac{d^2f(x)}{dx^2}+\frac{1}{a^3}\int_{-\infty}^{\infty}dx'exp(-\lambda|x-x'|)f(x')=\frac{b}{a^2}exp(-\lambda|x|)[/tex]

ofcourse Iv'e taken the Fourier tarnsform of both sides, but I don't see how to calcualte the Fourier tranform of the integral in the above equation, I feel I need to use the definition of dirac's delta function, but don't see how to do this, any ideas, hints?

thanks in advance.

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