A note on N. Bary’s one conjecture
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Shakro Tetunashvili
Abstract
A trigonometric sine series with special properties is constructed. One of the properties of this series shows that Bary’s conjecture on subsequences of partial sums of a sine series is not valid.
Dedicated to Prof. V. Kokilashvili on the occasion of his 80th birthday
References
[1] N. K. Bary, Subsequences converging to zero everywhere of partial sums of trigonometric series (in Russian), Izv. Akad. Nauk SSSR. Ser. Mat. 24 (1960), 531–548. Search in Google Scholar
[2] N. K. Bary, Trigonometric Series (in Russian), Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961. Search in Google Scholar
[3] G. Cantor, Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen, Math. Ann. 5 (1872), no. 1, 123–132. 10.1007/BF01446327Search in Google Scholar
[4] V. Y. Kozlov, On complete systems of orthogonal functions (in Russian), Mat. Sbornik (N.S.) 26 (1950), no. 68, 351–364. Search in Google Scholar
[5] S. T. Tetunashvili, On N. Bary’s one conjecture, Proc. A. Razmadze Math. Inst. 133 (2003), 164–165. Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture
