Geodesic
On absence conditions of unconditional bases of exponents
Ufa mathematical journal, Tome 7 (2015) no. 2, pp. 17-32

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In the classical space $L^2(-\pi,\pi)$ there exists the unconditional basis $\{e^{ikt}\}$ ($k$ is integer). In the work we study the existence of unconditional bases in weighted Hilbert spaces $L^2(I,\exp h)$ of the functions square integrable on an interval $I$ in the real axis with the weight $\exp(- h)$, where $h$ is a convex function. We obtain conditions showing that unconditional bases of exponents can exist only in very rare cases.
Keywords: Riesz bases, unconditional bases, series of exponents, Hilbert space
Mots-clés : Fourier–Laplace transform. 
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     author = {R. A. Bashmakov and A. A. Makhota and K. V. Trounov},
     title = {On absence conditions  of unconditional bases of exponents},
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2015_7_2_a1/}
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R. A. Bashmakov; A. A. Makhota; K. V. Trounov. On absence conditions  of unconditional bases of exponents. Ufa mathematical journal, Tome 7 (2015) no. 2, pp. 17-32. http://geodesic.mathdoc.fr/item/UFA_2015_7_2_a1/