As I know, The inverse of the inverse Laplace (or Fourier) transform of a function is equal to itself. Am I wrong?
and the inverse of the inverse Mellin transform of a function is equal to itself ?
The inverse of the inverse Mellin transform of a function is equal to itself?
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fourier-analysis
linear-transformations
laplace-transform
fourier-transform
1 Answers
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The inverse integral transform of an integral transform will get you back your original function except possibly for a set upon which the function of interest has a zero integral.
In particular, if a function has a finite number of discontinuities on any finite subinterval, you will lose information about those points because a discontinuity at a single point in a continuous neighborhood will not change the integral of that function.
Usually those points are not important, so we just refer to a transform and its inverse as essentially unique.