Weak spectral synthesis in Fourier algebras of coset spaces

Eberhard Kaniuth. "Weak spectral synthesis in Fourier algebras of coset spaces." Studia Mathematica 197.3 (2010): 229-246. <http://eudml.org/doc/285716>.

@article{EberhardKaniuth2010,
abstract = {Let G be a locally compact group, K a compact subgroup of G and A(G/K) the Fourier algebra of the coset space G/K. Applying results from [E. Kaniuth, Weak spectral synthesis in commutative Banach algebras, J. Funct. Anal. 254 (2008), 987-1002], we establish injection and localization theorems relating weak spectral sets and weak Ditkin sets for A(G/K) to such sets for A(H/H ∩ K), where H is a closed subgroup of G. We also prove some results towards the analogue of Malliavin's theorem for weak spectral synthesis in A(G/K) and give illustrating examples.},
author = {Eberhard Kaniuth},
journal = {Studia Mathematica},
keywords = {spectral set; set of synthesis; weak spectral set; Ditkin set; weak Ditkin set; Fourier algebra},
language = {eng},
number = {3},
pages = {229-246},
title = {Weak spectral synthesis in Fourier algebras of coset spaces},
url = {http://eudml.org/doc/285716},
volume = {197},
year = {2010},
}

TY - JOUR
AU - Eberhard Kaniuth
TI - Weak spectral synthesis in Fourier algebras of coset spaces
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 3
SP - 229
EP - 246
AB - Let G be a locally compact group, K a compact subgroup of G and A(G/K) the Fourier algebra of the coset space G/K. Applying results from [E. Kaniuth, Weak spectral synthesis in commutative Banach algebras, J. Funct. Anal. 254 (2008), 987-1002], we establish injection and localization theorems relating weak spectral sets and weak Ditkin sets for A(G/K) to such sets for A(H/H ∩ K), where H is a closed subgroup of G. We also prove some results towards the analogue of Malliavin's theorem for weak spectral synthesis in A(G/K) and give illustrating examples.
LA - eng
KW - spectral set; set of synthesis; weak spectral set; Ditkin set; weak Ditkin set; Fourier algebra
UR - http://eudml.org/doc/285716
ER -