Editing Dual lattice (section)

==Poisson summation formula==

The dual lattice is used in the statement of a general Poisson summation formula.
{{math theorem|
'''Theorem (Poisson Summation)'''<ref name="Cohn Kumar Reiher Schürmann 2013">{{cite book | last1=Cohn | first1=Henry | last2=Kumar | first2=Abhinav | last3=Reiher | first3=Christian | last4=Schürmann | first4=Achill | title=Discrete Geometry and Algebraic Combinatorics | chapter=Formal duality and generalizations of the Poisson summation formula | series=Contemporary Mathematics | year=2014 | volume=625 | pages=123–140 | doi=10.1090/conm/625/12495 | isbn=9781470409050 | s2cid=117741906 | arxiv=1306.6796v2 }}</ref>
Let <math display = "inline"> f : \mathbb{R}^n \to \mathbb{R} </math> be a [[Pathological (mathematics)|well-behaved]] function, such as a Schwartz function, and let <math display = "inline"> \hat{f} </math> denote its [[Fourier transform]]. Let <math display = "inline"> L \subseteq \mathbb{R}^n </math> be a full rank lattice. Then:

:<math> \sum_{x \in L} f(x) = \frac{1}{\det(L)} \sum_{y \in L^*} \hat{f}(y) </math>.
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<!--- let's get a text reference in here, also state more general conditions --->