Faltung Theorem

There is a useful theorem for the Fourier transform of a product of two functions, called the convolution theorem or the Faltung theorem iFaltung is German for folding ). The convolution of two functions fix) and g(x) is defined as the integral... 

Problem 1.2.2 Show that in the non-aging case, operator multiplication as defined by (1.2.10) is commutative. In fact, this is probably perceived more easily by using the alternative form, akin to matrix multiplication, derived from (1.2.32). The easiest way to show it is to take into account a result of Sect. 1.5, namely that in the frequency representation, operator multiplication becomes simple multiplication, by virtue of the Faltung theorem (Sect. A3.1). 

We seek here to generalize the observation contained in (1.5.1) to the three-dimensional context. Consider (1.8.9- 11). On taking Fourier transforms (FTs), these become, with the aid of the Faltung theorem [(A3.1.14- 17)] ... 

Convolution Theorem. The convolution (German Faltung, i.e. folding) of a function/(x) times a function with a different origin g(x) is the very useful... 

The Faltung or Convolution Theorem is a result of central importance for the Theory of Linear Viscoelasticity. It states that if... 

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