Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Le théorème des idempotents dans B(G). (The theorem of idempotents in B(G)) |
| Συγγραφείς: |
Host, B. |
| Στοιχεία εκδότη: |
Société Mathématique de France (SMF), Paris |
| Θεματικοί όροι: |
Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups, integer valued functions, idempotents, locally compact group, homomorphisms, \(L^p\)-spaces and other function spaces on groups, semigroups, etc, Fourier-Stieltjes algebra, Homomorphisms and multipliers of function spaces on groups, semigroups, etc |
| Περιγραφή: |
Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. This interesting paper gives a complete description of the integer valued functions in B(G). It turns out that these are exactly the linear combinations with integer coefficients of translates of characteristic functions of open subgroups of G. In particular, one thereby obtains a characterization of the idempotents in B(G). For discrete groups this theorem has been announced by \textit{M. Lefranc} [C. R. Acad. Sci., Paris, Sér. A 274, 1882-1883 (1972; Zbl 0247.43014)]. It is worth mentioning that Cohen's idempotent theorem for measures on abelian locally compact groups G can easily be deduced. In fact, \(B(G)=M(\Gamma)^{\wedge}\), where \({^{\wedge}}\) denotes Fourier transform and \(\Gamma\) the dual group of G. The author applies his result to describe homomorphisms from the Fourier algebra A(G) into B(H), where G and H are locally compact groups and, in addition, G is abelian. |
| Τύπος εγγράφου: |
Article |
| Περιγραφή αρχείου: |
application/xml |
| DOI: |
10.24033/bsmf.2055 |
| Σύνδεσμος πρόσβασης: |
https://zbmath.org/3979739 |
| Αριθμός Καταχώρησης: |
edsair.c2b0b933574d..68b444ec189b8d872acfe5b1b5d84a03 |
| Βάση Δεδομένων: |
OpenAIRE |