arXiv subjects

Juan Miguel Medina

Publications and source records attributed to Juan Miguel Medina.

3 recordsLinked to original sources

arXiv2026

Affine AP-frames and Stationary Random Processes

It is known that, in general, an affine or Gabor AP-frame is an $L^2(\mathbb{R})$-frame and conversely. In part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for an affine (wavelet) system $\mathcal{A}=\{a^{j/2} ψ_{j,k}(t):=a^{-j/2} ψ(a^{-j} t -k) :j\in\mathbb{Z}, k\in\mathbb{K}:=b\mathbb{Z}\}$ to be an affine AP-Frame in terms of Gaussian stationary random processes expanding in this way what we have done recently for Gabor systems. Likewise, we study a connection between the decay of the associated stationary sequences $\{\langle{X,ψ_{j,k}}\rangle : k\in\mathbb{K}\}$ for each $j\in\mathbb{Z}$, and a smoothness condition on a Gaussian stationary random process $X=(X(t))_{t\in\mathbb{R}}$.

math.PR↗

arXiv2017

Density of spaces of trigonometric polynomials with frequencies from a subgroup in $L^α$-spaces

Let $G$ be an LCA group, $H$ a closed subgroup, $\varGamma$ the dual group of $G$ and $μ$ be a regular finite non-negative Borel measure on $\varGamma$. We give some necessary and sufficient conditions for the density of the set of trigonometric polynomials on $\varGamma$ with frequencies from $H$ in the space $L^α(μ), α\in (0,\infty)$.

math.FA↗

arXiv2017

H-Regular Borel measures on locally compact abelian groups

Let $G$ be an LCA group, $H$ a closed subgroup, $\varGamma$ the dual group of $G$. In accordance with analogous notions in prediction theory the classes of $H$-regular and $H$-singular Borel measures on $Γ$ are defined. A characterization of $H$-regular measures is given and a Wold type decomposition is obtained.

math.FA↗