We answer a number of open problems in frame theory concerning the decomposition of frames into linearly independent and/or spanning sets. We prove that Parseval frames with norms bounded away from 1 can be decomposed into a number of sets whose complements are spanning, where the number of these sets only depends on the norm bound. Further, we prove a stronger result for Parseval frames whose ...

We develop a natural generalization of vector-valued frame theory, which we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointedness, compl...

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointeness, complementar...

We investigate the validity of Taylor's Hypothesis (TH) in analysis Alfv\'enic fluctuations velocity and magnetic fields solar wind streams measured by Parker Solar Probe (PSP)~during first four encounters. use PSP field measurements from 24 h intervals selected each The applicability TH is investigated measuring parameter $\epsilon=\delta u_0/\sqrt{2}V_\perp$, which quantifies ratio between ty...

We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on Hilbert space. As applications, we characterize affine Weyl-Heisenberg localization as well give uncertainty principles for the transforms.