this article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. we present a concrete formulation for the frobenius norm of the classical wavelet transforms over finite fields. it is shown that each vector defined over a finite field can be represented as...

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

this article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. it is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

We provide an explicit normal distinguished boundary dilation to a pair of commuting operators (S, P ) having the closed symmetrized bidisc Γ as a spectral set. This is called Sz.-Nagy dilation of (S, P ). The operator pair that dilates (S, P ) is obtained by an application of Stinespring dilation of (S, P ) given by Agler and Young. We further prove that the dilation is minimal and the dilatio...

The area of knowledge merging is concerned with merging conflicting information while preserving as much as possible. Most proposals in the literature work with knowledge bases expressed in propositional logic. We propose a new framework for merging knowledge bases expressed in (subsets of) first-order logic. Dilation operators (a concept originally introduced by Bloch and Lang) are employed an...