Unitary discrete Hilbert transforms

Two-dimensional Hilbert Transforms'

Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

A multidimensional discrete Hilbert-type inequality

In this paper, by using the way of weight coecients and technique of real analysis, a multidimensionaldiscrete Hilbert-type inequality with a best possible constant factor is given. The equivalentform, the operator expression with the norm are considered.

Polynomial Residue Systems via Unitary Transforms

A polynomial, A(z), can be represented by a polynomial residue system and, given enough independent residues, the polynomial can be reconstituted from its residues by the Chinese remainder theorem (CRT). A special case occurs when the discrete Fourier transform and its inverse realise the residue evaluations and CRT respectively, in which case the residue system is realised by the action of a m...

SVD compression, unitary transforms, and computational complexity

The search for fast unitary transforms and the need for data compression in linear systems are complementary issues. Compression requires the definition of a threshold dependent on the condition number, which is invariant over the unitary group. With respect tot this threshold it is shown that the SVD is the optimal tool. Considerations in connection with the Kronecker product and direct sum of...