In this work, a sort of binary wavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. Finitely Supported wavelet bases for Sobolev spaces is researched. Steming from a pair of finitely supported refinale functions with multi-scaled dilation factor in space 2 2 ( ) L R satsfying a very mild condition, we provide a novel method for designing ...

We study linear combinations of exponentials en, λn ∈ Λ in the case where the distance between some points λn tends to zero. We suppose that the sequence Λ is a finite union of uniformly discrete sequences. In (Avdonin and Ivanov, 2001), necessary and sufficient conditions were given for the family of divided differences of exponentials to form a Riesz basis in space L(0, T ). Here we prove tha...

Linear combinations of exponentials e iλ k t in the case where the distance between some points λ k tends to zero are studied. D. Ull-rich [30] has proved the basis property of the divided differences of exponentials in the case when {λ k } = Λ (n) and the groups Λ (n) consist of equal number of points all of them are close enough to n, n ∈ Z. We have generalized this result for groups with arb...

We prove that for any convex polytope $\Omega \subset \mathbb{R}^d$ which is centrally symmetric and whose faces of all dimensions are also symmetric, there exists a Riesz basis exponential functions in the space $L^2(\Omega)$. The result new $d$ greater than one.

We study the optimal approximation of the solution of an operator equation A(u) = f by certain n-term approximations with respect to specific classes of frames. We consider worst case errors, where f is an element of the unit ball of a Sobolev or Besov space Bt q(Lp(Ω)) and Ω ⊂ Rd is a bounded Lipschitz domain; the error is always measured in the Hs-norm. We study the order of convergence of th...

We study the optimal approximation of the solution of an operator equation A(u) = f by certain n-term approximations with respect to specific classes of frames. We consider worst case errors, where f is an element of the unit ball of a Sobolev or Besov space Bt q(Lp(Ω)) and Ω ⊂ Rd is a bounded Lipschitz domain; the error is always measured in the Hs-norm. We study the order of convergence of th...