Differentiable functions and their Fourier coefficients
Abstract
In the paper we consider the properties of Fourier coefficients of functions that possess derivatives of bounded variation. We investigate the convergence of the special series of Fourier coefficients with respect to general orthonormal systems (ONS). The obtained results are the best possible. We also describe the behavior of subsequences of general ONS.
References
[1] G. Alexits, Convergence Problems of Orthogonal Series, Int. Ser. Monogr. Pure Appl. Math. 20, Pergamon Press, New York, 1961. 10.1016/B978-1-4831-9774-6.50009-5Search in Google Scholar
[2] L. Gogoladze and V. Tsagareishvili, Fourier coefficients of continuous functions (in Russian), Mat. Zametki 91 (2012), no. 5, 691–703; translation in Math. Notes 91 (2012), no. 5-6, 645–656. 10.1134/S0001434612050057Search in Google Scholar
[3] S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Monogr. Math. 6, Chelsea, New York, 1951. Search in Google Scholar
[4] A. M. Olevskii, Orthogonal series in terms of complete systems (in Russian), Mat. Sb. (N. S.) 58(100) (1962), 707–748. Search in Google Scholar
[5] V. Tsagareishvili, Some properties of general orthonormal systems, Colloq. Math. 162 (2020), no. 2, 201–209. 10.4064/cm7857-9-2019Search in Google Scholar
[6]
V. S. Tsagareishvili,
Absolute convergence of Fourier series of functions of the class
[7] V. S. Tsagareishvili, On the Fourier coefficients of functions with respect to general orthonormal systems (in Russian), Izv. Ross. Akad. Nauk Ser. Mat. 81 (2017), no. 1, 183–202; translation in Izv. Math. 81 (2017), no. 1, 179–198. 10.1070/IM8394Search in Google Scholar
[8] V. S. Tsagareishvili, On the Fourier coefficients of functions with respect to general orthonormal systems (in Russian), Izv. Ross. Akad. Nauk Ser. Mat. 81 (2017), no. 1, 183–202; translation in Izv. Math. 81 (2017), no. 1, 179–198. 10.1070/IM8394Search in Google Scholar
[9] V. S. Tsagareishvili, General orthonormal systems and absolute convergence (in Russian), Izv. Ross. Akad. Nauk Ser. Mat. 84 (2020), no. 4, 208–220; translation in Izvestia Math. 84 (2020), no. 4, 816–828. 10.1070/IM8862Search in Google Scholar
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- Differentiable functions and their Fourier coefficients
Articles in the same Issue
- Frontmatter
- Spectral description of Fredholm operators via polynomially Riesz operators perturbation
- On the estimation of the Bernoulli regression function using Bernstein polynomials for group observations
- Mazurkiewicz sets with no well-ordering of the reals
- On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
- On the generalization of the Janashia–Lagvilava method for arbitrary fields
- On a boundary-domain integral equation system for the Robin problem for the diffusion equation in non-homogeneous media
- Classical inequalities for pseudo-integral
- The boundary value problem for one class of higher-order nonlinear partial differential equations
- On 𝑆-weakly prime ideals of commutative rings
- Necessary and sufficient conditions of optimality for second order discrete and differential inequalities
- Perturbation results and forward order law for the Moore–Penrose inverse in rings with involution
- On 𝑇1- and 𝑇2-productable compact spaces
- On a Riemann--Hilbert boundary value problem for (ϕ,ψ)-harmonic functions in ℝ m
- On an equation by primes with one Linnik prime
- Differentiable functions and their Fourier coefficients
