The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the "interpretation basis." This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determin...

This paper deals with the problem of continuoustime model identification and presents a subspace-based algorithm capable of dealing with data generated by systems operating in closed-loop. The algorithm is developed by reformulating the identification problem from the continuous-time model to an equivalent one to which discrete-time subspace identification techniques can be applied. More precis...

Wavelet analysis as a p–adic harmonic analysis Abstract New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers is considered. This map (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R) generated fro...

The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space, and using measurements which are products of projections onto this same orthonormal basis. In other words, neither entangled signal states nor entangled measur...

This article discusses the basic properties of finite-dimensional Boolean vector spaces and their linear transformations. We first introduce a natural Boolean-valued inner product and discuss orthonormal bases. We show that all bases are orthonormal and have the same cardinality. It is shown that the set of subspaces form an atomistic orthomodular poset. We then demonstrate that an operator tha...

Superconvergence of the gradient for the linear simplicial finite-element method applied to elliptic equations is a well known feature in one, two, and three space dimensions. In this paper we show that, in fact, there exists an elegant proof of this feature independent of the space dimension. As a result, superconvergence for dimensions four and up is proved simultaneously. The key ingredient ...

Multiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2’ + ’ and 2jcan be extracted by decomposing this signal on a wavelet orthonormal basis of L*(R”). In LL(R...

We consider self-similar measures µ with support in the interval 0 ≤ x ≤ 1 which have the analytic functions e i2πnx : n = 0, 1, 2,. .. span a dense subspace in L 2 (µ). Depending on the fractal dimension of µ, we identify subsets P ⊂ N 0 = {0, 1, 2,. .. } such that the functions {en : n ∈ P } form an orthonormal basis for L 2 (µ). We also give a higher-dimensional affine construction leading t...

This research concerns offline identification of acoustic characteristics of enclosures with second-order resonant dynamics and their modeling as linear dynamic systems. The applied models can be described by basis function expansions. The practical problem of acoustic echo in enclosures is used as the target problem to be addressed. It has been found out that the classical filters are ineffect...

We compare several properties and constructions of the Carlitz polynomials and digit derivatives for continuous functions on Fq[[T ]]. In particular, we show a close relation between them as orthonormal bases. Moreover, parallel to Carlitz’s coefficient formula, we give the closed formula for the expansion coefficients in terms of the digit derivatives.