Geodesic
Orthogonal bases for $L^p$ spaces
Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 375-385 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The spectrum of a system of functions which are orthogonal on $[0, 1]$ is the set of all $p\in[1,\infty]$ such that the system forms a basis in $L^p[0, 1]$ ($L^\infty=C$). A set $E$ is called a \underbar{spectral set} if there exists a system of functions orthonormal on $[0, 1]$ whose spectrum is $E$. In this note we determine all spectral sets and construct an orthonormal system corresponding to each of them. 
@article{MZM_1971_10_4_a1,
     author = {S. F. Gerasimov},
     title = {Orthogonal bases for $L^p$ spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {375--385},
     year = {1971},
     volume = {10},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a1/}
}
TY  - JOUR
AU  - S. F. Gerasimov
TI  - Orthogonal bases for $L^p$ spaces
JO  - Matematičeskie zametki
PY  - 1971
SP  - 375
EP  - 385
VL  - 10
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a1/
LA  - ru
ID  - MZM_1971_10_4_a1
ER  - 
%0 Journal Article
%A S. F. Gerasimov
%T Orthogonal bases for $L^p$ spaces
%J Matematičeskie zametki
%D 1971
%P 375-385
%V 10
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a1/
%G ru
%F MZM_1971_10_4_a1
S. F. Gerasimov. Orthogonal bases for $L^p$ spaces. Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 375-385. http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a1/