Abstract:
A frame for a vector space is a set of vectors which behaves in some
ways like a basis for the vector space while having a more flexible structure
that allows for frames to be constructed to fit a variety of application
situations, such as in signal processing. The frame potential function,
developed in 2001, takes a frame as input and returns its “frame potential
value”. This value reveals important information about the properties of
the input frame. In this paper, we adapt the frame potential function
to create a “relative frame potential function”, which takes one frame as
input with respect to another frame. We analyze the behavior of this
function to determine what information the relative frame potential value
can reveal about the relationship between the two frames.
