arXiv subjects
Publications and source records attributed to Ana Benavente.
Given an approximately continuous function $f$ in an Orlicz space $L^\Phi([a,b]),$ for a suitable class of convex functions $\Phi,$ we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in $L^\Phi([a,b]).$
We study uniqueness of best approximation in Orlicz spaces L$Φ$, for different types of convex functions $Φ$ and for some finite dimensional approximation classes of functions, where Tchebycheff spaces, and more general approximation ones, are involved
This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames $\{a^{j/2}ψ( a^j\cdot -kb)\}_{j,k\in \mathbb Z}$ in $L^2(\mathbb R)$ for which no dual frame has wavelet structure. We first generalize this result by proving that there exist wavelet frames for which no approximately dual frame has wavelet structure. Motivated by this we show that by imposing a very mild decay condition on the Fourier transform of the generator $ψ\in L^2(\mathbb R),$ a certain oversampling $\{a^{j/2}ψ( a^j\cdot -kb/N)\}_{j,k\in \mathbb Z}$ indeed has an approximately dual wavelet frame; most importantly, by choosing the parameter $N\in \mathbb N$ sufficiently large we can get as close to perfect reconstruction as desired, which makes the approximate dual frame pairs perform equally well as the classical dual frame pairs in applications.
The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We show that with this definition in many cases dual fusion frames behave similar to dual frames. We exhibit examples of non-canonical dual fusion frames.