a generalization of schauder basis associated with the concept of generalized analytic functions is introduced. corresponding concepts of density, completeness, biorthogonality and basicity are defined. also, corresponding concept of the space of coefficients is introduced. under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...

Abstract In this article, we introduce the notion of nonuniform biorthogonal wavelets on positive half line. We first establish characterizations for translates a single function to form Riesz bases their closed linear span. provide complete characterization biorthogonality scaling functions two multiresolution analysis and associated wavelet families in $$L^2({\mathbb {R}}^+)$$ <mml:math xmlns...

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable sepa...

We present the lifting scheme, a new idea for constructing compactly supported wavelets with compactly supported duals. The lifting scheme uses a simple relationship between all multiresolution analyses with the same scaling function. It isolates the degrees of freedom remaining after fixing the biorthogonality relations. Then one has full control over these degrees of freedom to custom design ...

This paper presents an error analysis of the Lanczos algorithm in finite-precision arithmetic for solving the standard nonsymmetric eigenvalue problem, if no breakdown occurs. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. The theory developed illustra...

Exceptional points and double poles of the S matrix are both characterized by the coalescence of a pair of eigenvalues. In the first case, the coalescence causes a defect of the Hilbert space. In the second case, this is not so as shown in previous papers. Mathematically, the reason for this difference is the biorthogonality of the eigenfunctions of a non-Hermitian operator that is ignored in t...

A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalues and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved ...