Related papers: On generalized Walsh bases
Let $C_h$ be a composition operator mapping $L^2(\Omega_1)$ into $L^2(\Omega_2)$ for some open sets $\Omega_1, \Omega_2 \subseteq \mathbb{R}^n$. We characterize the mappings $h$ that transform Riesz bases of $L^2(\Omega_1)$ into Riesz bases…
Representations of the Cuntz algebra $\mathcal{O}_N$ are constructed from interval dynamical systems associated with slow continued fraction algorithms introduced by Giovanni Panti. Their irreducible decomposition formulas are characterized…
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…
We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in…
Orthonormal systems in commutative $L_2$ spaces can be used to classify Banach spaces. When the system is complete and satisfies certain norm condition the unconditionality with respect to the system characterizes Hilbert spaces. As a…
A distinctive problem of harmonic analysis on $\R$ with respect to a Borel probability measure $\mu$ is identifying all $t\in\R$ such that both \[\left\{e^{-2\pi i\lambda x}: \lambda\in\Lambda\right\}\quad\text{and}\quad \left\{e^{-2\pi…
The conformal transformations with respect to the metric defining $o(n,\mbb{C})$ give rise to a nonhomogeneous polynomial representation of $o(n+2,\mbb{C})$. Using Shen's technique of mixed product, we generalize the above representation to…
A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand--Tsetlin patterns. Explicit formulas for the matrix elements…
In this paper we show how to construct a certain class of orthonormal bases in $L^2({\bf R}^d)$ starting from one or more Gabor orthonormal bases in $L^2({\bf R})$. Each such basis can be obtained acting on a single function…
We consider sparse representations of signals from redundant dictionaries which are unions of several orthonormal bases. The spark introduced by Donoho and Elad plays an important role in sparse representations. However, numerical…
The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^\lambda$ of $W$ corresponds to a standard module $M(\lambda)$ for…
As shown by Tropp, 2008, for the concatenation of two orthonormal bases (ONBs), breaking the square-root bottleneck in compressed sensing does not require randomization over all the positions of the nonzero entries of the sparse coefficient…
Apparently convergent contributions of resummed perturbative series at the next-to-leading order of the 1/N expansion in the O(N) model are reanalyzed in terms of renormalizability. Compared to our earlier article [G. Fejos et al., Phys.…
The aim of this note is to present some new explicit examples of $O(d,d)$-generalised Leibniz parallelisable spaces arising as the normal bundles of adjoint orbits $\mathcal{O}$ of some semi-simple Lie group $G$. Using this construction, an…
We study representations of the Cuntz algebras O_d and their associated decompositions. In the case that these representations are irreducible, their restrictions to the gauge-invariant subalgebra UHF_d have an interesting cyclic structure.…
We consider the problem in determining the countable sets $\Lambda$ in the time-frequency plane such that the Gabor system generated by the time-frequency shifts of the window $\chi_{[0,1]^d}$ associated with $\Lambda$ forms a Gabor…
We study unitary orthonormal bases in the sense of Pimsner and Popa for inclusions $(\mathcal{B}\subseteq \mathcal{A}, E),$ where $\mathcal{A}, \mathcal{B}$ are finite dimensional von Neumann algebras and $E$ is a conditional expectation…
Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to…