Geodesic
The Conjugate Function on the Finite Dimensional Torus
Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 140-148

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We consider the group T a , its group of characters Z a , and an arbitrary order P on Z a . For x ∊ Z a , let sgnp x be 1, - 1 , or 0 according as x € P\{0}, x € (-P)\{0}, or X = 0. For f in Lp (T a ), 1 < p < ∞, it is known that there is a function in Lp (T a ) such that for all X in Z a . Summability methods for are also available. In this paper, we obtain summability methods for that apply for in L1 (T a ), and we show how various properties of can be derived from our construction.
DOI : 10.4153/CMB-1989-021-5
Mots-clés : 43A55 
Asmar, Nakhle. The Conjugate Function on the Finite Dimensional Torus. Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 140-148. doi: 10.4153/CMB-1989-021-5
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     author = {Asmar, Nakhle},
     title = {The {Conjugate} {Function} on the {Finite} {Dimensional} {Torus}},
     journal = {Canadian mathematical bulletin},
     pages = {140--148},
     year = {1989},
     volume = {32},
     number = {2},
     doi = {10.4153/CMB-1989-021-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-021-5/}
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