Under certain assumptions we show that a wavelet frame {τ(Aj , bj,k)ψ}j,k∈Z := {|detAj |−1/2ψ(A−1 j (x− bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj,k are perturbed. As a special case of our result, we obtain that if {τ(Aj , ABn)ψ}j∈Z,n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {τ(Aj , ABλn)ψ}j∈Z,n∈Zd is a ...

The concept of g-frame is a natural extension the frame. This article mainly discusses relationship between some special bounded linear operators and g-frames, characterizes properties g-frames. In addition, according to operator spectrum theory, eigenvalues are introduced into new expression best frame boundary given.

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...