A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but
in certain approaches or applications a description in terms of a finite overcomplete system …

We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar
to frames in a Hilbert space, we show that for any two approximate Schauder frames for a …

Работа содержит обзор известных и доказательства новых результатов об условиях
на множество M в банаховом пространстве X, необходимых или достаточных для того …

We develop elements of a general dilation theory for operator-valued measures. Hilbert
space operator-valued measures are closely related to bounded linear maps on abelian von …

We prove that a sequence (fi) i= 1∞ of translates of a fixed f∈ L p (ℝ) cannot be an
unconditional basis of L p (ℝ) for any 1≤ p<∞. In contrast to this, for every 2< p<∞, d∈ ℕ …

Characterizations for a frame and its duals are known for separable Hilbert spaces. In this
paper, we characterize a class of approximate Schauder frame and its duals for separable …

A frame $(x_j) _ {j\in J} $ for a Hilbert space $ H $ is said to do phase retrieval if for all
distinct vectors $ x, y\in H $ the magnitudes of the frame coefficients $(|\langle x, x_j\rangle|) …

The Gaussian Gabor system at the critical density has the property that it is overcomplete in
$ L^ 2 (\mathbf {R}) $ by exactly one element, and if any single element is removed then the …

This paper studies Schauder frames in Banach spaces, a concept which is a natural
generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The …

We study conditions on a Banach frame that ensures the validity of a reconstruction formula.
In particular, we show that any Banach frames for (a subspace of) Lp or Lp, q (1≤ p<∞) with …