When we think of functions, we refer to their oscillations or periodic components in terms of frequencies. The Fourier transform allows us to decompose a function into its constituent frequencies, providing a way to analyze the function in the frequency domain.
For operators that act on infinite-dimensional function spaces, is there an analog of the frequency concept? Is there a transform or methodology that lets us analyze operators in a similar "frequency-centric" manner?
I'm curious about both theoretical constructs and any potential applications such a perspective might offer.