On the algebras $L_p$ of locally compact groups

Żelazko, W.

doi:10.4064/cm-8-1-115-120

Cited by 20 publications

(14 citation statements)

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“…This was conjectured by M. Rajagopalan in his 1963 Yale thesis, though the conjecture had already been settled in the abelian case by W.Żelazko [36]. Various authors, including Neil Rickert who was also a graduate student at Yale, made progress.…”

Section: Local Units In Fourier Algebrasmentioning

confidence: 93%

A Trip from Classical to Abstract Fourier Analysis

Ross¹

2014

Notices Amer. Math. Soc.

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C lassical Fourier analysis began withFourier series, i.e., the study of periodic functions on the real line R. Because trigonometric functions are involved, we will focus on 2π -periodic functions, which are determined by functions on [0, 2π ). This is a group under addition modulo 2π , and this group is isomorphic to the circle group T = {z ∈ C : |z| = 1} under the map t → e it . Classical results can be viewed as results on the compact abelian group T, and we will do so.Similarly, Fourier analysis on R n can be viewed as analysis on the locally compact 1 abelian (LCA) group R n . Our general setting will be a locally compact group G. Every such group has a (left) translationinvariant measure, called Haar measure because Alfred Haar proved this statement in 1932. For G = R n , this is Lebesgue measure. Haar measure for G = T is also Lebesgue measure, either on [0, 2π ) or transferred to the circle group T. Haar

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Section: Local Units In Fourier Algebrasmentioning

confidence: 93%

A Trip from Classical to Abstract Fourier Analysis

Ross¹

2014

Notices Amer. Math. Soc.

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“…Rickert [15] confirmed the conjecture for p = 2. For related results on the subject see also Crombez [1] and [2], Gaudet and Gamlen [3], Johnson [6], Kunze and Stein [7], Lohoue [8], Milnes [9], Rickert [14], and Zelazko [20]. Finally, in 1990, Saeki [16] gave an affirmative answer to the conjecture by a completely self-contained proof.…”

Section: Introductionmentioning

confidence: 94%

On the Lp-conjecture for locally compact groups

2007

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“…This latter statement, without the hypothesis 1(G) < oo, is the so called ^-conjecture, stated and discussed by Zelazko, Rajagopalan and others [3], [4], [5], [6], [7].…”

mentioning

confidence: 88%

On a certain invariant of a locally compact group

Leptin¹

1966

Bull. Amer. Math. Soc.

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On the algebras $L_p$ of locally compact groups

Cited by 20 publications

References 0 publications

A Trip from Classical to Abstract Fourier Analysis

A Trip from Classical to Abstract Fourier Analysis

On the Lp-conjecture for locally compact groups

On a certain invariant of a locally compact group

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