no. 3
A characterization of the minimal strongly character invariant Segal algebra
Annales de l'Institut Fourier, Tome 30 (1980) no. 3, pp. 129-139.

Pour un groupe abélien, localement compact G, on étudie l’espace S 0 (G), qui est formé de fonctions appartenant localement à l’algèbre de Fourier et se comportant à l’infini comme des éléments de l 1 . On donne une caractérisation abstraite de la famille des espaces {S 0 (G):G abélien} par ses propriétés héréditaires.

For a locally compact, abelian group G, we study the space S 0 (G) of functions on G belonging locally to the Fourier algebra and with l 1 -behavior at infinity. We give an abstract characterization of the family of spaces {S 0 (G):G abelian} by its hereditary properties.

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     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},
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     mrnumber = {82i:43004},
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}
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.795/

[1] J.P. Bertrandias, C. Datry, C. Dupuis, 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] J.P. Bertrandias, C. Dupuis, Transformation de Fourier sur les espaces lp (Lp′), Ann. Inst. Fourier, 29, Fasc. 1, (1979), 189-206. | EuDML | Numdam | MR | Zbl

[3] R. Bürger, Funktionen vom Verschiebungstyp und Segalalgebren, Dissertation, Wien 1979.

[4] R. Bürger, Functions of translation type and functorial properties of Segal algebras II, Preprint. | Zbl

[5] H.G. Feichtinger, A characterization of Wiener's algebra on locally compact groups, Arch. Math., 24 (1977), 136-140. | MR | Zbl

[6] H.G. Feichtinger, The minimal strongly character invariant Segal algebra I, II, Preprint.

[7] A. Grothendieck, Topological vector spaces, Gordon and Breach, New York-London-Paris, 1973. | MR | Zbl

[8] E. Hewitt, K.A. Ross, Abstract harmonic analysis I, Grundl. d. math. Wiss., Springer-Verlag, Berlin-Heidelberg-New York, 1963. | MR | Zbl

[9] F. Holland, Harmonic analysis on amalgams of Lp and lq, J. London Math. Soc., Ser II, 10 (1975), 295-305. | MR | Zbl

[10] J.P. Kahane, Séries de Fourier absolument convergentes, Ergebnisse d. Math., 50, Springer-Verlag, Berlin-Heidelberg-New York, 1970. | MR | Zbl

[11] H.E. Krogstad, Multipliers of Segal algebras, Math. Scand., 38 (1976), 285-303. | EuDML | MR | Zbl

[12] T.S. Liu, A. V. Rooij, J.K. Wang, On some group algebra modules related to Wiener's algebra M1, Pacific J. Math., 55 (1974), 507-520. | MR | Zbl

[13] H. Reiter, Classical harmonic analysis and locally compact groups, Oxford at the Clarendon Press, 1968. | MR | Zbl

[14] H.G. Feichtinger, 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] D. Poguntke, Gewisse Segalsche Algebren auf lokal-kompakten Gruppen, Arch. Math., 33 (1979), 454-460. | MR | Zbl

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