In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

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...

Wavelet packet transform decomposes a signal into a set of orthonormal bases (nodes) and provides opportunities to select an appropriate set of these bases for feature extraction. In this paper, multi-level basis selection (MLBS) is proposed to preserve the most informative bases of a wavelet packet decomposition tree through removing less informative bases by applying three exclusion criteria:...

We describe a space and time adaptive numerical method based on wavelet orthonormal bases for solving partial diierential equations. The multiresolution structure of wavelet orthonormal bases provides a simple way to adapt computational reenements to the local regularity of the solution 11] 16]. High resolution computations are performed only in regions where singularities or sharp transitions ...

We study the limit distribution of zeros of certain sequences of holomorphic sections of high powers L of a positive holomorphic Hermitian line bundle L over a compact complex manifold M . Our first result concerns ‘random’ sequences of sections. Using the natural probability measure on the space of sequences of orthonormal bases {SN j } of H(M,L ), we show that for almost every sequence {SN j ...

Orthonormal M-band wavelet bases have been constructed and applied by several authors. This paper makes three main contributions. First, it generalizes the minimal length Kregular 2-band wavelets of Daubechies to the M-band case by deriving explicit formulas for K-regular M-band scaling filters. Several equivalent characterizations of K-regularity are given and their significance explained. Sec...

The investigation of flutter and aeroservoelastic stability through flight testing is an essential part of aircraft certification. The stability boundary prediction is especially difficult when the instability is associated with nonlinearity in the dynamics. This paper presents an approach for the characterization of the nonlinear dynamics by non-iterative identification algorithms. Two differe...

In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...