Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...

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...

A provably stable reduced order model, based on a projection onto a scaled orthonormal Laguerre basis, followed by a SVD step, is proposed. The method relies on the conformal mapping properties induced by the complete orthonormal scaled Laguerre basis, allowing a mapping from the discrete-stable case to the continuous-stable case and vice versa.

The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a wavelet orthonormal basis. In wavelet orthonormal basis is a family of functions, which is built by dilating and translating a unique function. The development of orthonormal wa...

Any non-complete orthonormal system in a Hilbert space can be transformed into basis by small perturbations.