Criteria for Algebraic Operators to be Unitary

초록

By the spectral theorem, a unitary operator with a finite spectrum is algebraic and its spectrum is contained in T, the unit circle centered at 0. The most fundamental example of a unitary algebraic operator is the Fourier transform. According to the famous theorem of Plancherel, the Fourier transform extends uniquely to a unitary operator on L2(R) (see e.g., [18, Theorem IX.6]). Denote it by ". The Fourier transform has the following properties:

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