In spite of a detailed and nation-wide legislation frame, there exist large cantonal disparities in consumed quantities of health care services in Switzerland.
In the opposite direction, since ({f_{i}}_{iin J} ) is a frame for H, there exists a sequence ({c_{ell}}_{ellin J}inell^{2}(J) ) such that (e_{m}=sum_{ell in J}c_{ell}f_{ell}) for (min J ).
Given (gin L^{2}(mathbb {R})), the collection of functions ({E_{mb}T_{na}g }_{m,n in mathbb {Z}}) is called a (Gabor) frame if there exist constants (A,B>0) such that begin{aligned} A |f|^{2}lesum_{m,nin mathbb {Z}} bigl| langle f, E_{mb}T_{na}granglebigr|^{2} le B |f|^{2}, quadforall fin L^{2}(mathbb {R}).
Given two separable Hilbert spaces (H supseteq M ), suppose that ({x_{n} }_{nin J} ) is a Parseval frame for W. Then there exists an orthonormal basis ({e_{n}}_{nin J} ) for H s.t.
A choice frame is rationalizable if there exists a total pre-order R on Ω such that, for every E∈E, f(E) coincides with the best elements of E relative to R. We re-interpret choice structures in terms of belief revision.
In other words, signals at Points 1 – 4 decorrelate at adjacent frames, while there exist residual correlation at points 5 – 8 at adjacent frames.
There exists an orthonormal basis ({e_{i}}_{iin J} ) such that ({n_{i}}_{iin J}) is a Parseval frame if and only if there exists an antiunitary operator Λ such that (S_{omega} =Lambda SLambda^{-1}), where S is the frame operator of ({f_{i}}_{iin J} ).
It is known that for every frame ({E_{mb}T_{na}g }_{m,n in mathbb {Z}}), there exists a dual frame ({E_{mb}T_{na}h}_{m,nin mathbb {Z}}) such that each (fin L^{2}(mathbb {R})) has the decomposition begin{aligned} f=sum_{m,nin mathbb {Z}} langle f, E_{mb}T_{na}hrangle E_{mb}T_{na}h.
It means that there exists a frame ({eta_{i}}neq{S'psi_{i}}) for which f= {sum_{iinmathbb{Z}}langle f,eta_{i}rangle psi_{i}}, and ({eta_{i}}) is called the alternate dual frame of frame ({psi _{i}}).
