General Fourier coefficients and convergence almost everywhere
We find sufficient conditions which are in a sense best possible that must be satisfied by the functions of an orthonormal system in order for the Fourier coefficients of functions of bounded variation to satisfy the hypotheses of the Men’shov–Rademacher theorem. We also prove a theorem saying that...
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| Veröffentlicht in: | Izvestiya. Mathematics 2021-04, Vol.85 (2), p.228-240 |
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| container_end_page | 240 |
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| container_issue | 2 |
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| container_title | Izvestiya. Mathematics |
| container_volume | 85 |
| creator | Gogoladze, L. D. Cagareishvili, G. |
| description | We find sufficient conditions which are in a sense best possible that must be satisfied by the functions of an orthonormal system in order for the Fourier coefficients of functions of bounded variation to satisfy the hypotheses of the Men’shov–Rademacher theorem. We also prove a theorem saying that every system contains a subsystem with respect to which the Fourier coefficients of functions of bounded variation satisfy those hypotheses. The results obtained complement and generalize the corresponding results in [1]. |
| doi_str_mv | 10.1070/IM8985 |
| format | Article |
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| ispartof | Izvestiya. Mathematics, 2021-04, Vol.85 (2), p.228-240 |
| issn | 1064-5632 1468-4810 |
| language | eng |
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| source | Institute of Physics Journals; Alma/SFX Local Collection |
| subjects | Coefficient of variation Hypotheses Subsystems Theorems |
| title | General Fourier coefficients and convergence almost everywhere |
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