Sampling theorems on locally compact groups from oscillation estimates

局部紧群上Orlicz与混合范数Orlicz空间中非衰减信号的相关采样

Relevant sampling of non-decaying signals in Orlicz and mixed-norm Orlicz spaces defined on a locally compact group

本文针对局部紧群上非衰减信号，在加权Orlicz及混合范数Orlicz空间中建立确定性、平均及随机采样定理，并应用于平移不变空间与Orlicz调制空间。

Sampling theorems for the Heisenberg groups

In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part, attention is focussed on the simply connected nilpotent Heisenberg group $\HH$. We derive criteria for the existence of discretisations and sampling expansions associated to lattices in $\HH$. Analogies and differences to the sampling theorem over the reals are discussed, in particular a notion of bandwidth on $\HH$ will figure prominently. The main tools f…

LCA 群上拟平移不变空间中的随机平均采样

Random average sampling over quasi shift-invariant spaces on LCA groups

本文研究了局部紧阿贝尔群上混合 Lebesgue 空间中拟平移不变子空间的随机平均采样与重构问题，证明了当采样数足够大时，采样不等式和重构公式以极高概率成立。

Sampling in unitary invariant subspaces associated to LCA groups

In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of problems which are interesting in practice, avoiding also cumbersome notation. Along with LCA groups theory, the involved mathematical technique is that of frame theory which meets matrix analysis when appropriate dual frames are computed.

Sampling in reproducing kernel Banach spaces on Lie groups

We present sampling theorems for reproducing kernel Banach spaces on Lie groups. Recent approaches to this problem rely on integrability of the kernel and its local oscillations. In this paper we replace the integrability conditions by requirements on the derivatives of the reproducing kernel. The results are then used to obtain frames and atomic decompositions for Banach spaces of distributions stemming from a cyclic representation, and it is shown that this is particularly easy, when the cyclic vector is a Gårding vector for a square integrable representation.

Sampling and periodization of generators of Heisenberg modules

This paper considers generators of Heisenberg modules in the case of twisted group $C^*$-algebras of closed subgroups of locally compact abelian groups and how the restrction and/or periodization of these generators yield generators for other Heisenberg modules. Since generators of Heisenberg modules are exactly the generators of (multi-window) Gabor frames, our methods are going to be from Gabor analy\-sis. In the latter setting the procedure of restriction and periodization of generators is well known. Our results extend this established part of Gabor analy\-sis to the general setting of loc…