The Fourier series representation of a function is a classic representation which is widely used to approximate real functions (Stein & Shakarchi, 2003). In digital signal processing (Oppenheim & Schafer, 1975), the sampling theorem states that any real valued function f can be reconstructed from a sequence of values of f that are discretely sampled with a frequency at least twice as high as th...

In this work, the nonlinear boundary value problem in electrohydrodynamics flow of a fluid in an ion-drag configuration in a circular cylindrical conduit is studied numerically. An effective collocation method, which is based on orthonormal Bernstein polynomials is employed to simulate the solution of this model. Some properties of orthonormal Bernstein polynomials are introduced and utilized t...

Abstract In this paper, we consider some examples of set algebras $$ \mathcal{A} A on ℕ. If ℰ( ) is the simple functions , then ℒ ∗ α ( denotes ‖⋅‖ -closure ). Our aim to determine a complete orthonormal system for Hilbert space ∗2 in each regarded case. Here quotient modulo null-functions.

We exhibit the necessary range for which functions in Sobolev spaces L p s $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such Battle–Lemarié wavelets. also consider natural extensions to Triebel–Lizorkin spaces. This builds upon, and is a generalization of, previous work Seeger Ullrich, where analogous results were established Haar system.

Weaving frames have potential applications in wireless sensor networks that require distributed processing of signals under different frames. In this paper, we study some new properties weaving generalized (or g-frames) and orthonormal bases g-orthonormal bases). It is shown a g-frame its dual are woven. The inter-relation optimal bounds universal studied. Further, present characterization g-fr...

We study a class of orthonormal exponential bases for the space L2[0, 1] and introduce the concept of spectral sequences. We characterize piecewise linear spectral sequences with the knot at 1/2 and investigate the non-continuity of the piecewise linear spectral sequences. From a special construction of a piecewise constant spectral sequence, the classical Walsh system is recovered.

We present a scheme that leverage orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. The leveraged biorthogonal wavelets will have some nice properties. If we start with orthonormal wavelets, the leveraged scaling functions and wavelets are compactly supported and are diierentiable. The derivatives of the leveraged wavelets are orthogonal to their translations; the d...

We present a scheme that leverage orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. The leveraged biorthogonal wavelets will have some nice properties. If we start with orthonormal wavelets, the leveraged scaling functions and wavelets are compactly supported and are diierentiable. The derivatives of the leveraged wavelets are orthogonal to their translations; the d...

We consider a sequence HN of finite-dimensional Hilbert spaces of dimensions dN → ∞. Motivating examples are eigenspaces, or spaces of quasi-modes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of HN may be identified with U(dN), and a random orthonormal basis of is a choice of a random sequence UN∈U(dN) from the product of normal...

Orthonormal ridgelets are a specialized set of angularly-integrated ridge functions which make up an orthonormal basis for L2(R). In this paper we explore the relationship between orthonormal ridgelets and true ridge functions r(x1 cos θ + x2 sin θ). We derive a formula giving the ridgelet coefficients of a ridge function in terms of the 1-D wavelet coefficients of the ridge profile r(t), and w...