Lalit K. Vashisht

Banach Frames for Conjugate Banach Spaces

Retro Banach frames for conjugate Banach spaces have been introduced and studied. It has been proved that a Banach space E is separable if and only if E∗ has a retro Banach frame. Finally, a necessary and sufficient condition for a sequence in a separable Banach space to be a retro Banach frame has been given.

ON STABILITY OF BANACH FRAMES

Some stability theorems (Paley-Wiener type) for Banach frames in Banach spaces have been derived.

ON PERTURBATION OF BANACH FRAMES

A necessary and sufficient condition for the perturbation of a Banach frame by a non-zero functional to be a Banach frame has been obtained. Also a sufficient condition for the perturbation of a Banach frame by a sequence in E* to be a Banach frame has been given. Finally, a necessary condition for the perturbation of a Banach frame by a finite linear combination of linearly independent functionals in E* to be a Banach frame has been given.

On weaving fusion frames for Hilbert spaces

Very recently Bemrose et al. introduced a new concept of “weaving frames” in separable Hilbert spaces. Two frames {φ<inf>i</inf>}<inf>i∈I</inf> and {ψ<inf>i</inf>}<inf>i∈I</inf> for a separable Hilbert space ℍ are said to be woven, if there are universal positive constants A and B such that for every subset σ ⊂ I, the family {φ<inf>i</inf>}<inf>i∈σ</inf> ∪ {ψ<inf>i</inf>}<inf>i∈σc</inf> is a frame for ℋ with lower and upper frame bounds A and B, respectively. Weaving frames and fusion frames are connected with pre-processing and distributed data processing in signal analysis. In this paper, we present sufficient conditions for weaving fusion frames in separable Hilbert spaces. Paley-Wiener type perturbation results for weaving fusion frames are also given.

On continuous weaving frames

Abstract Two discrete frames { ϕ i } i ∈ I

The reconstruction property in Banach spaces generated by matrices

{\{\phi_{i}\}_{i\in I}}

Frames of Eigenfunctions Associated with a Boundary Value Problem

and { ψ i } i ∈ I

K

{\{\psi_{i}\}_{i\in I}}

\mathcal {K}

for a separable Hilbert space ℍ

-Matrix-valued Wave Packet Frames in L2(ℝd,ℂs×r)

{\mathbb{H}}