Stone's Theorem is a fundamental result in functional analysis that provides a framework for understanding the spectral properties of self-adjoint operators through functional calculus. It essentially states that any bounded self-adjoint operator can be represented via continuous functions on its spectrum, allowing us to extend the notion of functions acting on operators. This theorem is crucial for dealing with both bounded and unbounded self-adjoint operators, especially when considering their spectral characteristics.
congrats on reading the definition of Stone's Theorem. now let's actually learn it.