A characterization of the minimal strongly character invariant Segal algebra

Viktor Losert

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 3, page 129-139
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Losert, Viktor. "A characterization of the minimal strongly character invariant Segal algebra." Annales de l'institut Fourier 30.3 (1980): 129-139. <http://eudml.org/doc/74456>.

@article{Losert1980,
abstract = {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 $\lbrace S_0(G):G$ abelian$\rbrace $ by its hereditary properties.},
author = {Losert, Viktor},
journal = {Annales de l'institut Fourier},
keywords = {Segal algebra},
language = {eng},
number = {3},
pages = {129-139},
publisher = {Association des Annales de l'Institut Fourier},
title = {A characterization of the minimal strongly character invariant Segal algebra},
url = {http://eudml.org/doc/74456},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Losert, Viktor
TI - A characterization of the minimal strongly character invariant Segal algebra
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 3
SP - 129
EP - 139
AB - 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 $\lbrace S_0(G):G$ abelian$\rbrace $ by its hereditary properties.
LA - eng
KW - Segal algebra
UR - http://eudml.org/doc/74456
ER -

References

top
  1. [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. Zbl0365.46029MR81g:43005
  2. [2] J.P. BERTRANDIAS, C. DUPUIS, Transformation de Fourier sur les espaces lp (Lp′), Ann. Inst. Fourier, 29, Fasc. 1, (1979), 189-206. Zbl0387.42003MR82a:43006
  3. [3] R. BÜRGER, Funktionen vom Verschiebungstyp und Segalalgebren, Dissertation, Wien 1979. 
  4. [4] R. BÜRGER, Functions of translation type and functorial properties of Segal algebras II, Preprint. Zbl0461.43002
  5. [5] H.G. FEICHTINGER, A characterization of Wiener's algebra on locally compact groups, Arch. Math., 24 (1977), 136-140. Zbl0363.43003MR57 #7035
  6. [6] H.G. FEICHTINGER, The minimal strongly character invariant Segal algebra I, II, Preprint. 
  7. [7] A. GROTHENDIECK, Topological vector spaces, Gordon and Breach, New York-London-Paris, 1973. 
  8. [8] E. HEWITT, K.A. ROSS, Abstract harmonic analysis I, Grundl. d. math. Wiss., Springer-Verlag, Berlin-Heidelberg-New York, 1963. 
  9. [9] F. HOLLAND, Harmonic analysis on amalgams of Lp and lq, J. London Math. Soc., Ser II, 10 (1975), 295-305. Zbl0314.46029MR51 #11013
  10. [10] J.P. KAHANE, Séries de Fourier absolument convergentes, Ergebnisse d. Math., 50, Springer-Verlag, Berlin-Heidelberg-New York, 1970. Zbl0195.07602MR43 #801
  11. [11] H.E. KROGSTAD, Multipliers of Segal algebras, Math. Scand., 38 (1976), 285-303. Zbl0335.43004MR57 #10363
  12. [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. Zbl0303.43011
  13. [13] H. REITER, Classical harmonic analysis and locally compact groups, Oxford at the Clarendon Press, 1968. Zbl0165.15601MR46 #5933
  14. [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. Zbl0433.43002MR81e:43006
  15. [15] D. POGUNTKE, Gewisse Segalsche Algebren auf lokal-kompakten Gruppen, Arch. Math., 33 (1979), 454-460. Zbl0411.46040MR81e:43007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.