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Back to the Weyl Calculus

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

Abstract

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.

Keywords

Wigner Function Prime Divisor Fundamental Domain Dirichlet Series Integral Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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