Geodesic
À la recherche de la preuve perdue: a simple proof of the Ficken theorem
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014).

Voir la notice de l'article provenant de la source Library of Science

A new proof of the Ficken criterion is given together with a comment concerning the known proofs and related results 
@article{AUPCM_2014_13_a0,
     author = {Cicho\'n, Dariusz},
     title = {\`A la recherche de la preuve perdue: a simple proof of the {Ficken} theorem},
     journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
     publisher = {mathdoc},
     number = {13},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a0/}
}
TY  - JOUR
AU  - Cichoń, Dariusz
TI  - À la recherche de la preuve perdue: a simple proof of the Ficken theorem
JO  - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY  - 2014
IS  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a0/
LA  - en
ID  - AUPCM_2014_13_a0
ER  - 
%0 Journal Article
%A Cichoń, Dariusz
%T À la recherche de la preuve perdue: a simple proof of the Ficken theorem
%J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
%D 2014
%N 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a0/
%G en
%F AUPCM_2014_13_a0
Cichoń, Dariusz. À la recherche de la preuve perdue: a simple proof of the Ficken theorem. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014). http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a0/

[1] D. Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications 20, Birkhäuser Verlag, Basel, 1986. Cited on 133 and 134.

[2] A.S. Besicovitch, A problem on a circle, J. London Math. Soc. 36 (1961) 241-244 Cited on 134.

[3] C. Carathéodory, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo 32 (1911), 193-217. Cited on 135.

[4] A. Danelich, Normed spaces which satisfy Apollonius’ theorem, Mat. Zametki 20 (1976), 247-252. Cited on 136.

[5] M.M. Day, Normed Linear Spaces, Third edition, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21, Springer-Verlag, New York-Heidelberg, 1973. Cited on 134 and 135.

[6] N. Falkner, A characterization of inner product spaces Amer. Math. Monthly 100 (1993), no. 3, 246-249. Cited on 136.

[7] F.A. Ficken, Note on the existence of scalar products in normed linear spaces, Ann. of Math. (2) 45 (1944), 362-366. Cited on 134.

[8] V.I. Istratescu, Theory and applications, Mathematics and its Applications 25, D. Reidel Publishing Co., Dordrecht, 1987. Cited on 134.

[9] E.R. Lorch, On certain implications which characterize Hilbert space, Ann. of Math. (2) 49 (1948), 523-532. Cited on 133 and 134.