Fourier type transforms on Lie symmetry groups

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Journal Article
Journal of Mathematical Physics, 2015, 56 (9)
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© 2015 AIP Publishing LLC. In this paper, we construct operators on a Lie symmetry group which may be regarded as Fourier transforms. Essentially, we integrate solutions generated by Lie symmetries against suitable test functions. We show that this idea leads to a powerful method for solving Cauchy problems for parabolic and hyperbolic equations in two and higher dimensions. We also discuss applications to the elliptic case.
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