Uniqueness of uniform norm and C*-norm in L p(G, ω)

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Ibrahim Akbarbaglu ◽  
Majid Heydarpour ◽  
Saeid Maghsoudi
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Uniform Norm ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Weighted Algebra

AbstractLet G be a locally compact abelian group with a fixed Haar measure and ω be a weight on G. For 1 < p < ∞, we study uniqueness of uniform and C*-norm properties of the invariant weighted algebra L p(G, ω).

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

1987 ◽  
Vol 39 (1) ◽  
pp. 123-148 ◽  
Author(s):  
Maria L. Torres De Squire
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Dual Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
The Difference ◽  
Image Position

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

On Multipliers of the Group Lp;w(G)-Algebras

2013 ◽  
Vol 59 (2) ◽  
pp. 253-268
Author(s):  
Ilker Eryilmaz ◽  
Cenap Duyar
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact

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).

scholarly journals Multipliers on some weightedLp-spaces

2000 ◽  
Vol 23 (9) ◽  
pp. 651-656
Author(s):  
S. Öztop
Keyword(s):  
Abelian Group ◽  
Weight Function ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact

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).

On multipliers of Fourier transforms

1972 ◽  
Vol 71 (1) ◽  
pp. 63-66 ◽  
Author(s):  
Louis Pigno
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Lebesgue Space ◽  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Continuous Complex ◽  
Complex Valued

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.

Spans of translates in Lp(G)

1965 ◽  
Vol 5 (2) ◽  
pp. 216-233 ◽  
Author(s):  
R. E. Edwards
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Lebesgue Space ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Linear Combinations ◽  
Character Group ◽  
Weak Closure

Throughout this paper, G denotes a Hausdorff locally compact Abelian group, X its character group, and Lp(G) (1 ≦ p ≦ ∞) the usual Lebesgue space formed relative to the Haar measure on G. If f ∈ Lp(G), we denote by Tp[f] the closure (or weak closure, if p = ∞) in Lp(G) of the set linear combinations of translates of f.

On the equivalence of the properties of quasi-translation invariance and absolute continuity of measures on a locally compact abelian group

1987 ◽  
Vol 101 (2) ◽  
pp. 279-281
Author(s):  
Denis Bell
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Simple Proof ◽  
Compact Abelian Group ◽  
Absolute Continuity ◽  
Locally Compact Abelian Group ◽  
Translation Invariance ◽  
Positive Density ◽  
Locally Compact ◽  
Translation Invariant

AbstractWe give a simple proof that a measure on a locally compact abelian group G is quasi-translation invariant with continuous translation densities if and only if it is equivalent to Haar measure on G and has a continuous positive density.

The Wiener–Pitt phenomenon on semi-groups

1963 ◽  
Vol 59 (1) ◽  
pp. 11-24 ◽  
Author(s):  
T. A. Davis
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Haar Measure ◽  
Group Algebra ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Bounded Complex ◽  
Additive Measures ◽  
Complex Valued

Let G be a locally compact Abelian group, written adoptively, with Haar measure m, L1(G) the group algebra of G, and M(G) the Banach algebra of all bounded, complex-valued, regular, countably additive measures on G. For a general account of L1(G) and M(G) see Rudin (7).

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