Related papers: Properties of translates of frames on Vilenkin gro…
The aim of this paper is to study some properties of left translates of a square integrable function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a function $\varphi\in…
Let $G$ be a locally compact group with left regular representation $\lambda_{G}.$ We say that $G$ admits a frame of translates if there exist a countable set $\Gamma\subset G$ and $\varphi\in L^{2}(G)$ such that $(\lambda_{G}(x)…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
We construct the spectrum for a shift invariant space on Vilenkin group. We prove the results related to spectrum and Frame multiresolution analysis for Cantor dyadic group and Vilenkin group.
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…
Vilenkin groups, introduced by F. Ya Vilenkin, form a class of locally compact abelian groups. The present paper consists of the characterization of Parseval frame multiwavelets associated to multiresolution analysis (MRA) in the Vilenkin…
In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited…
We study square integrable functions on the metaplectic group and functions on the space of unitary symmetric matrices. We relate them using the oscillator representations.
We present elements of a theory of translation-invariant integration on finite dimensional vector spaces and on GL_n over a valuation field with local field as residue field. We then discuss the case of an arbitrary algebraic group. This…
Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates…
We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite dimensional $C^*$-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this…
We prove the equivalence of the frame property and the closedness for a weighted shift-invariant space. We also construct a sequence $\Phi^{2k+1}$ and the sequence of spaces $V^p_\mu(\Phi^{2k+1})$, $k\in{\mathbb{N}}$, on $\mathbb{R},$ with…
We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…
We introduce the concept of frame of multipliers in Hilbert modules over pro-C*-algebras and show that many properties of frames in Hilbert C*-modules are valid for frames of multipliers in Hilbert modules over pro-C*-algebras.
We consider the approximate properties of tight wavelet frames on Vilenkin group $G$. Let $\{G_n\}_{n\in \mathbb{Z} }$ be a main chain of subgroups, $X$ be a set of characters. We define a step function $\lambda({\chi})$ that is constant on…
A Hilbert module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert modules over a group C*-algebra which…
This is the abstract of the revised paper. The integrable XXZ model with a special open boundary condition is considered. We study Sklyanin transfer matrices after quantum group reduction in roots of unity. In this case Sklyanin transfer…
In this article we obtain families of frames for the space B_\omega of functions with band in [-\omega,\omega] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant,…