Hilbert space frame theory has applications to various areas of pure mathematics, applied mathematics, and engineering. However, the question of how applying an invertible operator to a frame changes its properties has not yet been satisfactorily answered, and only partial results are known to date. In this paper, we will provide a comprehensive study of those questions, and, in particular, pro...

In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...

Functional Gabor single-frame or multi-frame generator multipliers are the matrices of function entries that preserve Parseval generators. An interesting and natural question is how to characterize all such multipliers. This has been answered for several special cases including case generators in two dimensions one-dimension. In this paper we completely with respect separable time-frequency lat...

Frames are an essential tool for many emerging applications such as data transmission. Their main advantage is the fact that frames can be designed to be redundant while still providing reconstruction formulas. This makes them robust against noise and losses while allowing freedom in design (see, for example, [5, 10]). Due to their numerical stability, tight frames and Parseval frames are of in...

In [13] frames of subspaces extended to continuous version namely c-frame of subspaces. In this article we consider to the relations between cframes of subspaces and local c-frames. Also in this article we give some important relation about duality and parseval c-frames of subspaces.

New ideas were introduced in [3] to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.

Background Free-breathing whole-heart coronary MR angiography (MRA) is an established method that can visualize all coronary arteries within a single acquisition. However, a long acquisition time and suboptimal arterial signal due to thick SLAB are major limitations of 3T gradient-echo whole-heart coronary MRA without contrast. Alternatively, target-volume coronary MRA can be used to visualize ...

BACKGROUND AND PURPOSE 4D-MRA is a promising technique in the diagnosis and follow-up of cAVMs. The purpose of this study was to compare 4D-MRA in the pre- and postoperative evaluation of cAVMs with DSA or intraoperative findings as the standards of reference regarding qualitative and quantitative parameters. MATERIALS AND METHODS Fifty-six consecutive patients with cAVMs (30 women) underwent...

This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate lter banks and their applications to signal processing and especially compression. By their inherent structure, multiwavelets are t for processing multi-channel signals. First, we will recall some general results on multiwavelets and the convergence of the iterated matrix product. Then,...

The excess of a sequence in a Hilbert space H is the greatest number of elements that can be removed yet leave a set with the same closed span. This paper proves that if F is a frame for H and there exist infinitely many elements gn ∈ F such that F \ {gn} is complete for each individual n and if there is a uniform lower frame bound L for each frame F \ {gn}, then for each ε > 0 there exists an ...