Use Fourier transforms to solve the integral equation \[ \int _{-\infty }^{\infty } k(x-y)u(y)\,dy-u(x)=f(x) \] with \(k(x)=H(x)\), the Heaviside function.
Question
Math 6420 • PDE
Spring 2010 • Question 8
Question
Spring 2010 • Question 8
Use Fourier transforms to solve the integral equation \[ \int _{-\infty }^{\infty } k(x-y)u(y)\,dy-u(x)=f(x) \] with \(k(x)=H(x)\), the Heaviside function.