As a music chord is composed of different notes played unison, most
signals that reach us (sounds, biomolecules, electromagnetic waves or
stock prices) may be expressed as the sum of more basic components. In
mathematical terms a signal is regarded as a function that may also be
decomposed into more elementary ones which act as "building blocks".
Each "block" is associated with a specific "tone" and each tone corresponds,
mathematically speaking, to an eigenvalue.
On occasion one may be interested in highlighting or damping a
specific tone, for instance to enhance a particular sound. How well
such a tone can be isolated partly depends on the "distance" between the tones: The more
separated they are, the easier it is to distinguish them.
This talk will focus on the standard eigenvalues of a fractal called
the Sierpinski gasket, which can serve as a mathematical model for a
highly porous membrane. We will discuss how the distance between these
eigenvalues is related to the lowest eigenvalue, sometimes referred to
as the "fundamental tone" and discover that it is actually possible to
separate all tones.