Some generalizations of the Fourier and Hartley transforms on ℝ and ℝn are studied. These transforms involve functional coefficients. The Parseval identities, convolution formulas, conditions of self-adjointness and unitary property for new transforms are obtained.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 438, 2015, pp. 203–224.
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Petrov, V.E. Generalized Trigonometric Integral Transforms. J Math Sci 224, 135–149 (2017). https://doi.org/10.1007/s10958-017-3400-x
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DOI: https://doi.org/10.1007/s10958-017-3400-x