character group

2011 ◽  
Keyword(s):  
Character Group

scholarly journals Density and representation theorems for multipliers of type (p, q)

1967 ◽  
Vol 7 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Alessandro Figà-Talamanca ◽  
G. I. Gaudry
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Important Class ◽  
Lebesgue Spaces ◽  
Representation Theorems ◽  
Locally Compact ◽  
Bounded Linear ◽  
Character Group ◽  
Hausdorff Group ◽  
Lca Group

Let G be a locally compact Abelian Hausdorff group (abbreviated LCA group); let X be its character group and dx, dx be the elements of the normalised Haar measures on G and X respectively. If 1 < p, q < ∞, and Lp(G) and Lq(G) are the usual Lebesgue spaces, of index p and q respectively, with respect to dx, a multiplier of type (p, q) is defined as a bounded linear operator T from Lp(G) to Lq(G) which commutes with translations, i.e. τxT = Tτx for all x ∈ G, where τxf(y) = f(x+y). The space of multipliers of type (p, q) will be denoted by Lqp. Already, much attention has been devoted to this important class of operators (see, for example, [3], [4], [7]).

Singular measures with absolutely continuous convolution squares

1966 ◽  
Vol 62 (3) ◽  
pp. 399-420 ◽  
Author(s):  
Edwin Hewitt ◽  
Herbert S. Zuckerman
Keyword(s):  
Abelian Groups ◽  
Natural Order ◽  
Continuous Measure ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Character Group ◽  
Locally Compact Abelian Groups ◽  
Singular Measures ◽  
Compact Abelian Groups ◽  
Nikodym Derivative

Introduction. A famous construction of Wiener and Wintner ((13)), later refined by Salem ((11)) and extended by Schaeffer ((12)) and Ivašev-Musatov ((8)), produces a non-negative, singular, continuous measure μ on [ − π,π[ such thatfor every ∈ > 0. It is plain that the convolution μ * μ is absolutely continuous and in fact has Lebesgue–Radon–Nikodým derivative f such that For general locally compact Abelian groups, no exact analogue of (1 · 1) seems possible, as the character group may admit no natural order. However, it makes good sense to ask if μ* μ is absolutely continuous and has pth power integrable derivative. We will construct continuous singular measures μ on all non-discrete locally compact Abelian groups G such that μ * μ is a absolutely continuous and for which the Lebesgue–Radon–Nikodým derivative of μ * μ is in, for all real p > 1.

scholarly journals Coordinate sociogram analysis of interpersonal stress based on autosociometric modeling of interactive interaction

Ergodesign ◽  
2018 ◽  
Vol 2018 (2) ◽  
pp. 20-28 ◽  
Author(s):  
Михаил Сущенко ◽  
Mihail Sushchenko ◽  
Андрей Худяков ◽  
Andrey Hudyakov
Keyword(s):  
Group Interaction ◽  
Interpersonal Stress ◽  
Interactive Technologies ◽  
Character Group ◽  
The Social ◽  
Cartoon Character

The paper reports the principles of the social perceptive competence formation during comic perception. A possibility of the application of repertoire test of personal structures for the diagnostics of social perceptive capabilities is shown and empirically tested. The results of the experimental autosociometric estimate of the cartoon character group interaction are shown. The outlooks in the use of interactive technologies in the course of the social perceptive competences formation in designer- students are outlined.

On a Stein And Weiss Property of the Conjugate Function

1990 ◽  
Vol 42 (1) ◽  
pp. 109-125
Author(s):  
Nakhlé Asmar
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Conjugate Function ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Character Group ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
Image Position ◽  
Almost All

(1.1) The conjugate function on locally compact abelian groups. Let G be a locally compact abelian group with character group Ĝ. Let μ denote a Haar measure on G such that μ(G) = 1 if G is compact. (Unless stated otherwise, all the measures referred to below are Haar measures on the underlying groups.) Suppose that Ĝ contains a measurable order P: P + P ⊆P; PU(-P)= Ĝ; and P⋂(—P) =﹛0﹜. For ƒ in ℒ2(G), the conjugate function of f (with respect to the order P) is the function whose Fourier transform satisfies the identity for almost all χ in Ĝ, where sgnP(χ)= 0, 1, or —1, according as χ =0, χ ∈ P\\﹛0﹜, or χ ∈ (—P)\﹛0﹜.

Exponential Estimates for the Conjugate Function on Locally Compact Abelian Groups

1990 ◽  
Vol 33 (1) ◽  
pp. 34-44
Author(s):  
Nakhlé Habib Asmar
Keyword(s):  
Compact Support ◽  
Weak Type ◽  
Conjugate Function ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Character Group ◽  
Exponential Estimates ◽  
Compact Abelian Groups ◽  
The Hilbert Transform ◽  
Almost All

AbstractLet G be a locally compact Abelian group, with character group X. Suppose that X contains a measurable order P. For the conjugate function of f is the function whose Fourier transform satisfies the identity for almost all χ in X where sgnp(χ) = - 1 , 0, 1, according as We prove that, when f is bounded with compact support, the conjugate function satisfies some weak type inequalities similar to those of the Hilbert transform of a bounded function with compact support in ℝ. As a consequence of these inequalities, we prove that possesses strong integrability properties, whenever f is bounded and G is compact. In particular, we show that, when G is compact and f is continuous on G, the function is integrable for all p > 0.

scholarly journals On the continuity of the evaluation mapping associated with a group and its character group

1998 ◽  
Vol 126 (11) ◽  
pp. 3413-3415 ◽  
Author(s):  
Gerhard Turnwald
Keyword(s):  
Character Group

Finite Spaces of Signatures

1989 ◽  
Vol 41 (5) ◽  
pp. 808-829 ◽  
Author(s):  
Victoria Powers
Keyword(s):  
Quadratic Forms ◽  
Local Rings ◽  
Character Group ◽  
Witt Rings ◽  
Ordered Field ◽  
Spaces Of Orderings ◽  
Ordered Fields ◽  
Skew Fields ◽  
Finite Spaces ◽  
Field Setting

Marshall's Spaces of Orderings are an abstract setting for the reduced theory of quadratic forms and Witt rings. A Space of Orderings consists of an abelian group of exponent 2 and a subset of the character group which satisfies certain axioms. The axioms are modeled on the case where the group is an ordered field modulo the sums of squares of the field and the subset of the character group is the set of orders on the field. There are other examples, arising from ordered semi-local rings [4, p. 321], ordered skew fields [2, p. 92], and planar ternary rings [3]. In [4], Marshall showed that a Space of Orderings in which the group is finite arises from an ordered field. In further papers Marshall used these abstract techniques to provide new, more elegant proofs of results known for ordered fields, and to prove theorems previously unknown in the field setting.

character group

2006 ◽  
pp. 196-196
Keyword(s):  
Character Group
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