The biorthogonality condition for Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders is derived. This condition, is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding Stokes flow problem.

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 ...

In the scalar case, computation of recurrence coeecients of polynomials orthogonal with respect to a nonnegative measure is done via modiied Chebyshev algorithm. Using the concept of matrix biorthogonality, we extend this algorithm to the vector case.

The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...

After brieey reviewing the interrelation between Riesz-bases, biorthogonality and a certain stability notion for multiscale basis transformations we establish a basic stability criterion for a general Hilbert space setting. An important tool in this context is a strengthened Cauchy inequality. It is based on direct and inverse estimates for a certain scale of spaces induced by the underlying mu...

The rise of frame theory in appled mathematics is due to the flexibility and redundancy of frames. Structured frames are much easier to construct than Structured orthonormal bases. In this work, the notion of the ternary generalized multiresolution structure (TGMS) of subspace 2 3 ( ) L R is proposed, which is the generalization of the ternary frame multiresolution analysis. The biorthogonality...