Orthogonal systems of spline wavelets as unconditional bases in Sobolev spaces

Cubic Spline Wavelet Bases of Sobolev Spaces and Multilevel Intorpolation

In this paper, it is constructed that a semi-orthogonal cubic spline wavelet basis of homogeneous Sobolev space H 2 0 (I), which turns out to be a basis of continuous space C 0 (I). Meanwhile, the orthogonal projections on the wavelet subspaces in H 2 0 (I) are extended to the interpolating operators on the corresponding wavelet subspaces in C 0 (I). It is also given that a fast discrete wavele...

Uniqueness of Unconditional Bases in Banach Spaces

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique uncondit...

Unconditional Bases and Unconditional Finite-dimensional Decompositions in Banach Spaces

Let X he a Banach space with an unconditional finite-dimensional Schauder decomposition (En). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each En. For example, we show that if sup,, dim En < c~ and X has Gordon-Lewis local unconditional s t ructure then X has an unconditional basis ...

Polynomials on Banach Spaces with Unconditional Bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of...

Riesz Bases in Sobolev Spaces 1792 Hb