Abstract Harmonic Analysis: Volume 1

@inproceedings{Wall1963AbstractHA,
  title={Abstract Harmonic Analysis: Volume 1},
  author={C. T. C. Wall and Edwin Shields Hewitt and Kenneth A. Ross},
  year={1963}
}
Compact connected abelian groups of dimension 1
The compact connected abelian groups of dimension 1 are represented and classified in an efficient and explicit way. Main tools are Pontryagin Duality and the Resolution Theorem for compact abelianExpand
The main decomposition of finite-dimensional protori
Abstract A protorus is a compact connected abelian group of finite dimension. We use a result on finite-rank torsion-free abelian groups and Pontryagin duality to considerably generalize a well-knownExpand
LACUNARITY FOR COMPACT GROUPS. II
DERIVATIONS ON MATRIX ALGEBRAS WITH APPLICATIONS TO HARMONIC ANALYSIS
In this paper, the derivations between ideals of the Banach algebra $\frak {E}$$_\infty(I)$ are characterized. Necessary and sufficient conditions for weak amenability of Banach algebras $\frakExpand
WELL-KNOWN LCA GROUPS CHARACTERIZED BY THEIR CLOSED SUBGROUPS1
In this paper we determine (1) the class of all nondiscrete LCA groups for which every proper closed subgroup is the kernel of a continuous character of the group, (2) the class of locally compactExpand
Asymptotically Stationary and Related Processes
We survey the known properties of asymptotically stationary processes and discuss their relationship with other processes with finite variances. The appropriate notions of asymptotic stationarity,Expand
On dense embeddings of discrete groups into locally compact groups
We consider a class of discrete groups which have no ergodic actions by translations on continuous non-compact locally compact groups. We also study dense embeddings ofZn (n>1) into non-compactExpand
Discrete Spectrum of Nonstationary Stochastic Processes on Groups
Vector-valued, asymptotically stationary stochastic processes on σ-compact locally compact abelian groups are studied. For such processes, we introduce a stationary spectral measure and show that itExpand
Certain averages on the -adic numbers
For LP n L2 functions f, with p greater than one, defined on the a-adic numbers Qa, we consider averages like A"l)f(x)= -E 1 (x +n2a) and A(2)f(x)=Z fE(x+Pna), n=1 n=l where x and a are in a*. HereExpand
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