Back to the Weyl Calculus

Part of the Pseudo-Differential Operators book series (PDO, volume 1)


We come back to the constructions of Section 3: our standing assumption in this chapter is that the number N is 4 times a squarefree odd integer, but it does not have to coincide with 4 or 12 any more. Then, not every element of (ℤ/Nℤ)× is a square, and we have to consider the full set of distributions ϖρ as defined in Lemma 3.2: we introduce the linear combination
$$ W_N \left( {x,\xi } \right) = \sum\limits_{\rho \in R_N } {W\left( {\varpi _\rho ,\varpi _\rho } \right)\left( {x,\xi } \right)} , $$
again a Γ-invariant distribution. Recall that ? is the set of squares in (ℤ/Nℤ)× and that R N is a set of representatives of (ℤ/Nℤ)× mod Λ.


Wigner Function Prime Divisor Fundamental Domain Dirichlet Series Integral Kernel 
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© Birkhäuser Verlag AG 2008

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