In this case, the Green's function is the same as the impulse response of linear time-invariant system theory.

It is well known that sinusoidal signals are eigenfunctions of linear, and time-invariant systems.

In applied mathematics, semigroups are fundamental models for linear time-invariant systems.

A high-pass filter is usually modeled as a linear time-invariant system.

When the variable is time, they are also called time-invariant systems.

The application to linear time-invariant systems is well known.

Common examples of linear time-invariant systems are most electronic and digital filters.

Therefore, the behavior of a linear time-invariant system can be analyzed at each frequency independently.

It investigates the response of a linear and time-invariant system to an arbitrary input signal.

For time-invariant linear systems in the state space representation, a convenient test to check if a system is observable exists.