scholarly journals Multipliers for Amalgams and the Algebra S0(G)

1987 ◽  
Vol 39 (1) ◽  
pp. 123-148 ◽  
Author(s):  
Maria L. Torres De Squire

Throughout the whole paper G will be a locally compact abelian group with Haar measure m and dual group Ĝ. The difference of two sets A and B will be denoted by A ∼ B, i.e.,For a function f on G and s ∊ G, the functions f′ and fs will be defined by

Author(s):  
R. C. Baker

AbstractThe following generalization of a theorem of Weyl appeared in part I of this series of papers. Let G be a locally compact Abelian group with dual group ĝ. Let be a sequence in ĝ, not too slowly growing in a certain precise sense. Then, provided ĝ has ‘not too many’ elements of finite order, the sequencesare uniformly distributed on the circle, for almost all x in G.


1973 ◽  
Vol 9 (1) ◽  
pp. 73-82 ◽  
Author(s):  
U.B. Tewari ◽  
A.K. Gupta

Let G be a locally compact abelian group and Ĝ be its dual group. For 1 ≤ p < ∞, let Ap (G) denote the set of all those functions in L1(G) whose Fourier transforms belong to Lp (Ĝ). Let M(Ap (G)) denote the set of all functions φ belonging to L∞(Ĝ) such that is Fourier transform of an L1-function on G whenever f belongs to Ap (G). For 1 ≤ p < q < ∞, we prove that Ap (G) Aq(G) provided G is nondiscrete. As an application of this result we prove that if G is an infinite compact abelian group and 1 ≤ p ≤ 4 then lp (Ĝ) M(Ap(G)), and if p > 4 then there exists ψ є lp (Ĝ) such that ψ does not belong to M(Ap (G)).


1959 ◽  
Vol 11 (4) ◽  
pp. 195-206 ◽  
Author(s):  
J. H. Williamson

Let G be a locally compact Abelian group, and the set of bounded complex (regular countably-additive Borel) measures on G. It is well known that becomes a Banach space if the norm is defined bythe supremum being over all finite sets of disjoint Borel subsets of G.


2003 ◽  
Vol 68 (2) ◽  
pp. 345-350
Author(s):  
R. Nair

Let S be a semigroup contained in a locally compact Abelian group G. Let Ĝ denote the Bohr compactification of G. We say that a sequence contained in S is Hartman uniform distributed on G iffor any character χ in Ĝ. Suppose that (Tg)g∈s is a semigroup of measurable measure preserving transformations of a probability space (X, β, μ) and B is an element of the σ-algebra β of positive μ measure. For a map T: X → X and a set A ⊆ X let T−1A denote {x ∈ X: Tx ∈ A}. In an earlier paper, the author showed that if k is Hartman uniform distributed thenIn this paper we show that ≥ cannot be replaced by =. A more detailed discussion of this situation ensues.


2013 ◽  
Vol 59 (2) ◽  
pp. 253-268
Author(s):  
Ilker Eryilmaz ◽  
Cenap Duyar

Abstract Let G be a locally compact abelian group (non-compact, non-discrete) with Haar measure and 1 ≤ p < ∞: The purpose of this paper is to study the space of multipliers on Lp;w (G) and characterize it as the algebra of all multipliers of the closely related Banach algebra of tempered elements in Lp;w (G).


1966 ◽  
Vol 18 ◽  
pp. 389-398 ◽  
Author(s):  
Daniel Rider

Let G be a compact abelian group and E a subset of its dual group Γ. A function ƒ ∈ L1(G) is called an E-function if for all γ ∉ E wheredx is the Haar measure on G. A trigonometric polynomial that is also an E-function is called an E-polynomial.


2000 ◽  
Vol 23 (9) ◽  
pp. 651-656
Author(s):  
S. Öztop

LetGbe a locally compact abelian group with Haar measuredx, and letωbe a symmetric Beurling weight function onG(Reiter, 1968). In this paper, using the relations betweenpiandqi, where1<pi,   qi<∞,pi≠qi(i=1,2), we show that the space of multipliers fromLωp(G)to the spaceS(q′1,q′2,ω−1), the space of multipliers fromLωp1(G)∩Lωp2(G)toLωq(G)and the space of multipliersLωp1(G)∩Lωp2(G)toS(q′1,q′2,ω−1).


Author(s):  
Louis Pigno

In this paper G is a locally compact Abelian group, φ a complex-valued function defined on the dual Γ, Lp(G) (1 ≤ p ≤ ∞) the usual Lebesgue space of index p formed with respect to Haar measure, C(G) the set of all bounded continuous complex-valued functions on G, and C0(G) the set of all f ∈ C(G) which vanish at infinity.


1966 ◽  
Vol 6 (1) ◽  
pp. 65-75 ◽  
Author(s):  
R. E. Edwards

SummaryLet G denote a Hausdorff locally compact Abelian group which is nondiscrete and second countable. The main results (Theorems (2.2) and (2.3)) assert that, for any closed subset E of G there exists a pseudomeasure s on G whose singular support is E; and that if no portion of E is a Helson set, then such an s may be chosen having its support equal to E. There follow (Corollaries (2.2.4) and (2.3.2)) sufficient conditions for the relations to hold for some pseudomeasure s, E and F being given closed subsets of G. These results are analogues and refinements of a theorem of Pollard [4] for the case G = R, which asserts the existence of a function in L∞(R) whose spectrum coincides with any preassigned closed subset of R.


Sign in / Sign up

Export Citation Format

Share Document