P-woven frames.

The known family of woven collections of frames have interesting properties and applications. Yet, they cannot be easily constructed. The present paper introduces new collections of frames sharing many properties with the original ones and having simpler construction. The frames { φ i } i ∈ I and { ψ i } i ∈ I for a Hilbert space H are called partition-woven (or briefly P-woven), if there exists a nontrivial subset σ of I such that the family { g i } i ∈ I represented as the triple ({ φ i } , { ψ i } , σ) and called a P-weaven frame, is a frame defined by g i = φ i if i ∈ σ and g i = ψ i , otherwise. The paper also studies the class of CP-woven collections of frames which is a subset of the P-woven collections of frames and satisfy a stronger condition. The set of all woven frames is a strict subset of the set of all CP-woven frames which is further a strict subset of the set of all P-woven frames. Several examples and counterexamples are studied to show whether or not a pair of frames is P-woven or CP-woven. [ABSTRACT FROM AUTHOR]