Landau’s Necessary Density Conditions for Lca Groups
نویسنده
چکیده
We derive necessary conditions for sampling and interpolation of bandlimited functions on a locally compact abelian group in line with the classical results of H. Landau for bandlimited functions on R. Our conditions are phrased as comparison principles involving a certain canonical lattice.
منابع مشابه
Optimal Sampling and Reconstruction in Multiple - Input - Multiple - Output ( MIMO ) Systems 1
We consider a sampling scheme where a set of multiband input signals are passed through a MIMO liner time-invariant system and the outputs are sampled. MIMO sampling is a very general scheme that encompasses various other schemes, including Papoulis’ generalized sampling and nonuniform sampling as special cases. We present necessary density conditions for stable MIMO sampling. These results gen...
متن کاملClassification of self-dual torsion-free LCA groups
In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of selfdual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-du...
متن کاملOn component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملA homomorphism theorem for bilinear multipliers
In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...
متن کاملA Property of the Haar Measure of Some Special LCA Groups
The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...
متن کامل