Two Inner Sequences Based Invariant Subspaces in $${{H}^{2} (\mathbb{D}^{2})}$$ H 2 ( D 2 )

Approximation from shift - invariant subspaces of L 2 ( IR d )

Abstract: A complete characterization is given of closed shift-invariant subspaces of L2(IR) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating f...

Approximation from Shift - Invariant Subspaces of L 2 ( R d )

In this report, a summary of [1] is given. In [1] the authors provide a complete characterization of closed shift-invariant subspaces of L2(R) and the corresponding approximation order. The characterization of principal shift-invariant spaces is given in terms of the Fourier transform of the generator. The approximation order of a general shift-invariant space is the same as a suitably chosen p...

Frames and Stable Bases for Shift-invariant Subspaces of L 2 (ir D ) Frames and Stable Bases for Shift-invariant Subspaces of L 2 (ir D )

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : `2(X)! H : c 7! X

Extending Functions in the Model Subspaces of H^2(R) to C

Complemented Invariant Subspaces and Interpolation Sequences

It is shown that the invariant subspace of the Bergman space Ap of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in Ap. Let D be the open unit disc of the complex plane C, and let H = H(D) denote the usual Hardy space. For 0 < p < ∞ the Bergman space A consists of analytic functions f on D such that ‖f‖p = ∫ D |f(z)| dA(z) < ∞, where dA is area mea...