Full-spark frames arising from one-parameter groups.

The present paper provides a procedure for constructing full-spark Parseval frames arising from the linear action of a 1-parameter group acting in R n . Precisely, given a square matrix A of order n, with real entries, we say that A induces the full spark frame property if the following conditions hold. There exists a vector v for which given any finite set X ⊂ R of cardinality n, the collection { exp ⁡ (x A) v : x ∈ X } is a basis for R n . First, we show that if the spectrum of A is not a subset of the reals, then A does not induce the full spark frame property. Secondly, we establish that if the spectrum of A is a subset of the reals, then A induces the full spark frame property if and only if every eigenvalue of A has geometric multiplicity one. The proof of the latter fact gives a new algorithm for the construction of a class of full spark Parseval frames for R n . [ABSTRACT FROM AUTHOR]