# Boundary value problem for Hemlholtz equation with pseudospectral method.

I have an equation of the form $$(1-0.1 \Delta)f=1$$ with boundary condition $$f=0$$. I need to solve it for $$f$$ by pseudospectral method in python. Apparently, it should be $$f=\frac{1}{1-0.1\Delta}$$. I know that by fourier and inverse fourier transform i can get laplace operator but i am confused that the fourier tranform works in a way, that if you have a function $$f$$, you take its fourier tranform $$f_{k}$$ then multiply it with $$-k^2$$ which will give you $$\Delta f_k$$ and then using inverse fourier transform we get $$\Delta f$$. But i am supposed to find $$f$$ from the equation then if dont have $$f$$ initially how can i compute its fourier ransform and how can i get the inverse operator $$\frac{1}{1-0.1 \Delta}$$ using fourier tranform theory?