We show that a nested sequence of C macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H(Ω), 1 < s < r+ 3 2 , and H 0(Ω), 1 < s < σ+ 3 2 , s / ∈ Z+ 1 2 , as soon as there is a nested sequence of Lagrange interpolation sets with uniformly local and bounded basis functions, and, in case of H 0(Ω), the nodal interpolation operators ...

We use the matrix-valued Fejér–Riesz lemma for Laurent polynomials to characterize when a univariate shift-invariant space has a local orthonormal shift-invariant basis, and we apply the above characterization to study local dual frame generators, local orthonormal bases of wavelet spaces, and MRA-based affine frames. Also we provide a proof of the matrixvalued Fejér–Riesz lemma for Laurent pol...

In this note we present a review, some considerations and new results about maps with values in distribution space domain σ-finite measure X. Namely, is survey Bessel maps, frames bases (in particular Riesz Gel’fand bases) space. setting, the Riesz-Fischer semi-frames are defined them obtained. Some examples tempered distributions examined.

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literature on this topic.

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

We introduce multipulse multicarrier (MPMC) modulation, a wireless communication scheme that augments traditional singlepulse multicarrier systems by using multiple pulses at the transmitter and the receiver. The mathematical foundation of MPMC systems is established by the novel concept of multipulse Gabor Riesz bases. We adapt Zak-Fourier domain tools previously developed for multiwindow Gabo...

Recently we developed multiscale spaces of C piecewise quadratic polynomials relative to arbitrary polygonal domains Ω ⊂ R. These multiscale bases are weakly stable with respect to the L2 norm. In this paper we show that these bases form strongly stable Riesz bases for the Sobolev spaces Hs(Ω) with s ∈ (2, 5 2 ).

In recent investigation 8] concerning the asymptotic behavior of Gram Schmidt or-thonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in L 2 (IR +) arose. In this note, we provide a suucient condition to determine whether the nonnegative translates form a Riesz system on L 2 (IR +)....