Geodesic
Generalized trigonometric integral transformations
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 203-224

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We study some generalizations of the Fourier and Hartley transformations on $\mathbb R$ and $\mathbb R^n$. These transformations involve functional coefficients. The Parceval identities, convolution formulas, conditions of selfadjointness and unitary property for new transformations are obtained. 
@article{ZNSL_2015_438_a12,
     author = {V. E. Petrov},
     title = {Generalized trigonometric integral transformations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {203--224},
     publisher = {mathdoc},
     volume = {438},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a12/}
}
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V. E. Petrov. Generalized trigonometric integral transformations. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 203-224. http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a12/