Geodesic
Long-time evolution described by the unitary group of the Mehler operator
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 98-112

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In this work the long-time asymptotics of the solution to the Cauchy problem is described by means of the evolution unitary group of the self-adjoint Mehler operator. Spectral analysis of the latter operator is also discussed. 
@article{ZNSL_2021_506_a9,
     author = {M. A. Lyalinov},
     title = {Long-time evolution described by the unitary group of the {Mehler} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--112},
     publisher = {mathdoc},
     volume = {506},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a9/}
}
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M. A. Lyalinov. Long-time evolution described by the unitary group of the Mehler operator. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 98-112. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a9/