On the constancy of signs and order of magnitude of Fourier–Haar coefficients
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Larry Gogoladze
Abstract
In the paper, we investigate the relation between the properties of functions and their Fourier–Haar coefficients. We show that for some classes of functions Fourier–Haar coefficients have constant signs and order of magnitude.
In 1964, Golubov proved in [B. I. Golubov,
On Fourier series of continuous functions with respect to a Haar system (in Russian),
Izv. Akad. Nauk SSSR Ser. Mat. 28 1964, 1271–1296] that if
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: FR/102/5-100/14
Funding statement: The work was supported by the Shota Rustaveli National Science Foundation grant number FR/102/5-100/14.
References
[1] G. Alexits, Convergence Problems of Orthogonal Series, Internat. Ser. Monogr. Pure Appl. Math. 20, Pergamon Press, New York, 1961. 10.1016/B978-1-4831-9774-6.50009-5Search in Google Scholar
[2] B. I. Golubov, On Fourier series of continuous functions with respect to a Haar system (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1271–1296. Search in Google Scholar
[3] V. Tsagareishvili, On the order of magnitude of Haar–Fourier coefficients, Anal. Math. 35 (2009), 301–316. 10.1007/s10476-009-0405-9Search in Google Scholar
[4] P. L. Ul’janov, On Haar series (in Russian), Mat. Sb. (N.S.) 63(105) (1964), 356–391. Search in Google Scholar
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- Semilinear fractional order integro-differential inclusions with infinite delay
- Quasi-nilpotent perturbations of the generalized Kato spectrum
- Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
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- On the constancy of signs and order of magnitude of Fourier–Haar coefficients
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- Approximation by bivariate (p,q)-Baskakov–Kantorovich operators
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- A note on the Borel types of some small sets
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- Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras
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Articles in the same Issue
- Frontmatter
- Semilinear fractional order integro-differential inclusions with infinite delay
- Quasi-nilpotent perturbations of the generalized Kato spectrum
- Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
- Relations between BV*(q;α) and Λ*BVp classes of functions
- On the constancy of signs and order of magnitude of Fourier–Haar coefficients
- On the oscillatory behavior of solutions of higher order nonlinear fractional differential equations
- Optimal control problem for the equation of vibrations of an elastic plate
- Generalized Hausdorff capacities and their applications
- Approximation by bivariate (p,q)-Baskakov–Kantorovich operators
- A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field
- A note on the Borel types of some small sets
- On some boundary value problems for the heat equation in a non-regular type of a prism of ℝN+1
- Some weighted integral inequalities for differentiable h-preinvex functions
- Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras
- On Baer invariants of pairs of groups
- The Arzelà–Ascoli theorem by means of ideal convergence
- Absolute convergence of multiple Fourier series of a function of p(n)-Λ-BV
