Gabor Multipliers are linear operators arising similar to Fourier multipliers: Given an input signal the Gabor expansions is obtained. After multiplication with a sequence of numbers the synthesis operator is applied. From an engineering point of view they are like actions of an audio-engineer who decides in a time-variant manner who the different frequency bands of a signal are amplified or damped.

In the mathematical description one deals with function spaces, classes of operators, symbols etc.. For example, the question of best approximation of a given Hilbert Schmidt-operator by Gabor multipiers (in the Hilbert Schmidt norm) is translated into an approximation problem for spline-type functions (comparable to the question of approximating an $L^2$-function on $R$ by a cubic spline function).

Gabor multipliers are easily implemented and even the theory of discrete Gabor multipliers provides a non-trivial and interesting chapter of linear algebra.