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- W163036911 abstract "The main point of the chapter is a development of the theory of transmutation operators on the phase space associated to the Heisenberg group. The basic constructions heavily depend on many properties of Laguerre functions. They arise as eigenfunctions of the special Hermite operator (mathfrak{L}) . A number of important properties of Laguerre functions and their generalizations are proved at the beginning of the chapter. A holomorphic extension of the discrete Fourier–Laguerre transform leads to the transform ℱ l (p,q) , which is an analog of the spherical transform in the case under consideration. The basic properties of this transform are studied. In particular, the Paley–Wiener theorem for ℱ l (p,q) is proved using the Koornwinder integral representation of Jacobi functions for Laguerre functions. Then transmutation operators on ℂ n associated with the Laguerre polynomials expansion are investigated." @default.
- W163036911 created "2016-06-24" @default.
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- W163036911 date "2009-01-01" @default.
- W163036911 modified "2023-09-25" @default.
- W163036911 title "The Case of Phase Space" @default.
- W163036911 doi "https://doi.org/10.1007/978-1-84882-533-8_12" @default.
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