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The Balian-Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(t-na)\}_{m,n \in \mbox{\bf Z}}$
      
The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
This phenomena is related to the invariant cycles under the transformation We also give a characterization of all low-pass filters for MSF wavelets.
      
The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
We also give a characterization of all low-pass filters for MSF wavelets.
      
Unitary mappings between multiresolution analyses of L2 (R) and a parametrization of low-pass filters
      
These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L2([-π, π)), which we characterize.
      
We characterize the wavelet multipliers, as well as the scaling function multipliers and low pass filter multipliers.
      
The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series.
      
The characterization of low pass filters and some basic properties of wavelets, scaling functions and related concepts
      
Only certain smooth classes of the low pass filters that are determined by these scaling functions, however, appear to be characterized in the literature (see Chapter 7 of [3] for an account of these matters).
      
This somewhat technical result does provide a method for simple constructions of low pass filters whose only smoothness assumption is a Holder condition at the origin.
      
We apply our general results to special linear groups and low rank symmetric groups, and obtain new efficient algorithms for harmonic analysis on these classes of groups, as well as the two-sphere.
      
An Inhomogeneous Uncertainty Principle for Digital Low-Pass Filters
      
Related fundamental principles in Gabor analysis are also surveyed, including the Wexler-Raz biorthogonality relations, the Duality Principle, the Balian-Low Theorem, the Walnut and Janssen representations, and the Homogeneous Approximation Property.
      
These decompositions have a multiscale structure, independent Gaussian random variables in high-frequency terms, and the random coefficients of low-frequency terms approximating the Gaussian stationary process itself.
      
Convolution Estimates and Model Surfaces of Low Codimension
      
Prodigiosin also could induce apoptosis of pancreatic cancer cells at low concentration and results in the fragmentation pattern of DNA.
      
VEGF, microalbuminuria, HbA1c, creatinine, triglycerides, total cholesterol, fasting serum glucose, high-density lipoprotein (HDL), and low-density lipoprotein (LDL) were measured.
      
Furthermore, at low concentrations (up to 5 mM), Me2SnCl2 binds to the phosphate groups of DNA in an exothermic step and had no significant effect on double-strand DNA stability, confirmed by the fact that the Tm value did not change.
      
 

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