On convergence subsystems of orthonormal systems |
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| Authors: | G Bareladze |
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| Institution: | (1) Faculty of Mechanics and Mathematics, I. Javakhishvili Tbilisi State University, 2, University St., 380043 Tbilisi, Republic of Georgia |
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| Abstract: | It is proved that for any sequence {R
k}
k=1
of real numbers satisfyingR
k k (k1) andR
k=o(k log2
k),k , there exists an orthonormal system { n
k(x)}
n=1
,x (0;1), such that none of its subsystems {n
k(x)}
k=1
withn
k Rk (k1) is a convergence subsystem. |
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| Keywords: | 42C20 |
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