Frame theory is an active research area in mathematics, computer science and engineering with many exciting applications a variety of different fields. In this paper we study the notion dual continuous K-frames Hilbert spaces. Also establish some properties.

In this note we will show that the so called Sobolev dual is the minimizer over all linear reconstructions using dual frames for stable r order Σ∆ quantization schemes under the so called White Noise Hypothesis (WNH) design criteria. We compute some Sobolev duals for common frames and apply them to audio clips to test their performance against canonical duals and another alternate dual correspo...

Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications Gabor systems, wavelets, coorbit theory, and sensor modeling. In recent years, the computing associated deviations canonical alternate from original ones has been considered by functional analysts. this paper, we consider quantitative measurement approximately ones. More precisely, it is proved t...

In this article, we discuss some recent developments on pairs of dual wavelet frames in Sobolev spaces constructed by the Oblique Extension Principle (OEP) from refinable function vectors. Our investigation sheds a new light on understanding the OEP method for constructing MRA dual wavelet frames.