Metaplectic group, symplectic Cayley transform, and fractional Fourier transforms. (English) Zbl 1322.43003

At the beginning of the paper, the authors give a survey of the theory of metaplectic operators and their Maslov indices. Then they proceed to Weyl representation of metaplectic operators. In particular, they introduce the Cayley transform for symplectic matrices, which allows one to study the spreading functions of metaplectic operators. Applications to the Schrödinger equation and fractional Fourier transform are given.


43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
42C99 Nontrigonometric harmonic analysis
42C15 General harmonic expansions, frames
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