Geodesic
Bases of exponentials, sines and cosines in weighted spaces on a~finite interval
Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 413-443

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain a result concerning the basis property in a weighted space on an interval $(-a,a)$ for a system of exponentials generated by the zeros of the Fourier transform of a function with singularities at the ends of the support interval $(-a,a)$. For an arbitrary $\Delta\in\mathbb{C}$ we find a criterion for the basis property of the system $(e^{i(n+\Delta\operatorname{sign} n)t})_{n\in\mathbb{Z}}$ in a weighted space on the interval $(-\pi,\pi)$ and the systems of sines $(\sin((n+\Delta)t))_{n\in\mathbb{N}}$ and cosines $1\cup (\cos((n+\Delta)t))_{n\in\mathbb{N}}$ in a weighted space on the interval $(0,\pi)$. The weight is everywhere a finite product of polynomial functions.
Keywords: bases of exponentials, weighted spaces. 
@article{IM2_2011_75_2_a7,
     author = {S. S. Pukhov},
     title = {Bases of exponentials, sines and cosines in weighted spaces on a~finite interval},
     journal = {Izvestiya. Mathematics },
     pages = {413--443},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a7/}
}
TY  - JOUR
AU  - S. S. Pukhov
TI  - Bases of exponentials, sines and cosines in weighted spaces on a~finite interval
JO  - Izvestiya. Mathematics 
PY  - 2011
SP  - 413
EP  - 443
VL  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a7/
LA  - en
ID  - IM2_2011_75_2_a7
ER  - 
%0 Journal Article
%A S. S. Pukhov
%T Bases of exponentials, sines and cosines in weighted spaces on a~finite interval
%J Izvestiya. Mathematics 
%D 2011
%P 413-443
%V 75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a7/
%G en
%F IM2_2011_75_2_a7
S. S. Pukhov. Bases of exponentials, sines and cosines in weighted spaces on a~finite interval. Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 413-443. http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a7/