On everywhere divergence of trigonometric Fourier series
Journal Article
·
· Sbornik. Mathematics
- M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
The following theorem is established. Theorem. Let a function {phi}:[0,+{infinity}){yields}[0,+{infinity}) and a sequence {l_brace}{psi}(m){r_brace} satisfy the following condition: the function {phi}(u)/u is non-decreasing on (0,+{infinity}), {psi}(m){>=}1 (m=1,2,...) and {phi}(m){psi}(m)=o(m{radical}ln m / {radical}ln ln m) as m{yields}{infinity}. Then there is a function f element of L[-{pi},{pi}] such that {integral}{sub -{pi}}{sup {pi}}{phi}(|f(x)|) dx<{infinity} and lim sup{sub m{yields}}{sub {infinity}}S{sub m}(f,x)/{psi}(m)={infinity} for all x element of [-{pi},{pi}] here S{sub m}(f) is the m-th partial sum of the trigonometric Fourier series of f.
- OSTI ID:
- 21202904
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 1 Vol. 191; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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