Pour un groupe abélien, localement compact , on étudie l’espace , qui est formé de fonctions appartenant localement à l’algèbre de Fourier et se comportant à l’infini comme des éléments de . On donne une caractérisation abstraite de la famille des espaces abélien par ses propriétés héréditaires.
For a locally compact, abelian group , we study the space of functions on belonging locally to the Fourier algebra and with -behavior at infinity. We give an abstract characterization of the family of spaces abelian by its hereditary properties.
@article{AIF_1980__30_3_129_0, author = {Losert, Viktor}, title = {A characterization of the minimal strongly character invariant {Segal} algebra}, journal = {Annales de l'Institut Fourier}, pages = {129--139}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {30}, number = {3}, year = {1980}, doi = {10.5802/aif.795}, mrnumber = {82i:43004}, zbl = {0425.43003}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.795/} }
TY - JOUR AU - Losert, Viktor TI - A characterization of the minimal strongly character invariant Segal algebra JO - Annales de l'Institut Fourier PY - 1980 SP - 129 EP - 139 VL - 30 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.795/ DO - 10.5802/aif.795 LA - en ID - AIF_1980__30_3_129_0 ER -
%0 Journal Article %A Losert, Viktor %T A characterization of the minimal strongly character invariant Segal algebra %J Annales de l'Institut Fourier %D 1980 %P 129-139 %V 30 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.795/ %R 10.5802/aif.795 %G en %F AIF_1980__30_3_129_0
Losert, Viktor. A characterization of the minimal strongly character invariant Segal algebra. Annales de l'Institut Fourier, Tome 30 (1980) no. 3, pp. 129-139. doi : 10.5802/aif.795. http://www.numdam.org/articles/10.5802/aif.795/
[1] Unions et intersections d'espaces L invariantes par translation ou convolution, Ann. Inst. Fourier, 28, Fasc. 2, (1978), 53-84. | EuDML | Numdam | MR | Zbl
, , ,[2] Transformation de Fourier sur les espaces lp (Lp′), Ann. Inst. Fourier, 29, Fasc. 1, (1979), 189-206. | EuDML | Numdam | MR | Zbl
, ,[3] Funktionen vom Verschiebungstyp und Segalalgebren, Dissertation, Wien 1979.
,[4] Functions of translation type and functorial properties of Segal algebras II, Preprint. | Zbl
,[5] A characterization of Wiener's algebra on locally compact groups, Arch. Math., 24 (1977), 136-140. | MR | Zbl
,[6] The minimal strongly character invariant Segal algebra I, II, Preprint.
,[7] Topological vector spaces, Gordon and Breach, New York-London-Paris, 1973. | MR | Zbl
,[8] Abstract harmonic analysis I, Grundl. d. math. Wiss., Springer-Verlag, Berlin-Heidelberg-New York, 1963. | MR | Zbl
, ,[9] Harmonic analysis on amalgams of Lp and lq, J. London Math. Soc., Ser II, 10 (1975), 295-305. | MR | Zbl
,[10] Séries de Fourier absolument convergentes, Ergebnisse d. Math., 50, Springer-Verlag, Berlin-Heidelberg-New York, 1970. | MR | Zbl
,[11] Multipliers of Segal algebras, Math. Scand., 38 (1976), 285-303. | EuDML | MR | Zbl
,[12] On some group algebra modules related to Wiener's algebra M1, Pacific J. Math., 55 (1974), 507-520. | MR | Zbl
, , ,[13] Classical harmonic analysis and locally compact groups, Oxford at the Clarendon Press, 1968. | MR | Zbl
,[14] Un espace de Banach de distributions tempérées sur les groupes localement compacts abélien, C.R.A.S. Paris, t. 290, Série A (1980), 791-794. | MR | Zbl
,[15] Gewisse Segalsche Algebren auf lokal-kompakten Gruppen, Arch. Math., 33 (1979), 454-460. | MR | Zbl
,Cité par Sources :