Exact(60)
(Inversion formula).
(The Lagrange inversion formula).
The Möbius inversion formula [3] is defined as follows.
The Kuznecov transform and Kuznecov inversion formula play a central role in the proof of this Whittaker Plancherel inversion formula.
where the last equality is due to the matrix inversion formula.
To see (2.10) we apply the (distributional) Fourier inversion formula to (2.8).
The measure can be reconstructed from by means of the inversion formula.
In Sect. 4 we prove linearity and discuss an inversion formula.
For the case of, the matrix inversion formula allows us to instead write (35).
In the following lemma, we give the Lagrange inversion formula, which was proved by Stanley [4].
The basic properties including the inversion formula for this transform are studied.
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