Consider the following integral equation. \exp \left(-b x^{2}\right)=\int_{-\infty}^{\infty} \exp \left(-a\left(x-x^{\prime}\right)^{2}\right) \phi\left(x^{\prime}\right) d x^{\prime} where aand b are real positive numbers and a > b. OBy Fourier transforming both sides of

the above equation, obtain the Fourier transform (k) of ó(x). [5] Invert the Fourier transform (k) to obtain ø(x). [4] For a → b, what function is ó(x)? Verify that this function satisfies the integral equation when a = b. [1]