An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of ...

Optimization problems in the fuzzy environment are widely studied literature. We restrict our attention to mathematical programming with coefficients and/or decision variables expressed by numbers. Since review of recent literature on shows that extension principle is present through arithmetic but much less involved foundations solution concepts, we believe efforts rehabilitate idea following ...

We extend Hardy’s uncertainty principle for a square integrable function ψ and its Fourier transform to the n-dimensional case using a symplectic diagonalization. We use this extension to show that Hardy’s uncertainty principle is equivalent to a statement on the Wigner distribution Wψ of ψ. We give a geometric interpretation of our results in terms of the notion of symplectic capacity of an el...

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...

We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter-wave, microwave, optical, and Mössbauer clock tests, yields comprehensi...