Gabor-type expansions on local fields (Q1735721)

The paper deals with Gabor frames on local fields of positive characteristics. The author establishes necessary and sufficient conditions for two families of Gabor functions in $L^2(K)$ to yield orthogonal or bi-orthogonal expansions. The conditions are given in terms of some simple equations in the frequency domain. \par The paper is well-organized. It contains an exhaustive introduction. The proofs are technical. Linguistic mistakes slightly disturb the reading.