Task: Text Categorization
Input (English): This operation is an automorphism of the Schwartz space and, by duality, the space of tempered distributions. This operation restricted to the dense subspace formed by the intersection of the L 1 and L 2  spaces is a linear isometry into L 2 according to the Plancherel theorem, which can be used to prove its uniqueness. The integral over the reals of the squared modulus of a function f is equal to the integral over the reals of the squared modulus of this operation applied to f, which is equivalent to the fact that this operation is unitary, according to Parseval's relation. This transform is integrated over the reals and is defined using a complex exponential. For 10 points, identify this operation that transforms a time- domain function to one in the frequency-domain, and which shares many properties with the Laplace transform.
Output (English): Science