Weighted discrete convolution algebras

1983 ◽  
pp. 295-300 ◽  
Author(s):  
Niels Grønbæk
Keyword(s):  
Discrete Convolution ◽  
Convolution Algebras

Amenability of weighted discrete convolution algebras on cancellative semigroups

1988 ◽  
Vol 110 (3-4) ◽  
pp. 351-360 ◽  
Author(s):  
Niels Grønbæk
Keyword(s):  
Approximate Identity ◽  
Discrete Convolution ◽  
Convolution Algebra ◽  
Convolution Algebras ◽  
Approximate Identities

SynopsisIn this paper we apply a theorem of Khelemskiĭ and Sheĭnberg, characterising amenability by means of bounded approximate identities, to weighted discrete convolution algebras. In doing this we give a condition for a weighted discrete convolution algebra to have a bounded approximate identity. Under the condition that the semigroup (S,.) is one-sided cancellative, we prove that, if some weighted discrete convolution algebra on S is amenable, then (S,.) is actually a group. We further characterise all amenable weighted discrete convolution algebras on groups, thus extending a well-known theorem of B. E. Johnson [9].

scholarly journals BIFLATNESS AND BIPROJECTIVITY OF BANACH ALGEBRAS GRADED OVER A SEMILATTICE

2010 ◽  
Vol 52 (3) ◽  
pp. 479-495
Author(s):  
NIELS GRØNBÆK ◽  
FEREIDOUN HABIBIAN
Keyword(s):  
Banach Algebra ◽  
Necessary Conditions ◽  
Banach Algebras ◽  
Sufficient Conditions ◽  
Discrete Convolution ◽  
Convolution Algebras

AbstractWe give sufficient conditions and necessary conditions for a Banach algebra, which is ℓ1-graded over a semi-lattice, to be biflat or biprojective. As an application we characterise biflat and biprojective discrete convolution algebras for commutative semi-groups.

scholarly journals On a family of weighted convolution algebras

1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli
Keyword(s):  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Asymptotic Estimates ◽  
Locally Compact ◽  
Invariance Properties ◽  
Beurling Algebra ◽  
Convolution Algebras ◽  
Approximate Identities ◽  
Beurling Algebras ◽  
Banach Ideals

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.

A Fast Method for Solving Contact Plasticity in a Half Space

2011 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Residual Stresses ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Three Dimensional ◽  
New Method ◽  
Fast Method ◽  
Discrete Convolution ◽  
Influence Coefficients ◽  
The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

scholarly journals Amenability of Convolution Algebras.

1996 ◽  
Vol 79 ◽  
pp. 283 ◽  
Author(s):  
A. T. -m. Lau ◽  
R. J. Loy
Keyword(s):  
Convolution Algebras
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