On the absolute convergence of Fourier series with respect to general orthonormal systems
-
Vakhtang Tsagareishvili
Abstract
The problems of absolute convergence of multiple Fourier series with respect to both general orthonormal systems and multiple Haar series are studied.
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] S. V. Bočkarev, Absolute convergence of Fourier series in complete orthogonal systems (in Russian), Uspekhi Mat. Nauk 27 (1972), no. 2(164), 53–76. 10.1070/RM1972v027n02ABEH001371Search in Google Scholar
[3] L. Gogoladze and V. Tsagareishvili, On the divergence of Fourier series of functions in several variables, Anal. Math. 39 (2013), no. 3, 163–178. 10.1007/s10476-013-0301-1Search 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
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Impulsive differential inclusions via variational method
- Frame properties of a part of an exponential system with degenerate coefficients in Hardy classes
- A note on two-variable Chebyshev polynomials
- Spectral analysis of dissipative fractional Sturm–Liouville operators
- Common best proximity pairs in strictly convex Banach spaces
- Traces of Muckenhoupt weighted function spaces in case of distant singularities
- The commutativity of prime Γ-rings with generalized skew derivations
- Δμ-sets and ∇μ-sets in generalized topological spaces
- On strong well-posedness of initial-boundary value problems for higher order nonlinear hyperbolic equations with two independent variables
- Area properties associated with a convex plane curve
- Almost semi-correspondence
- The generalization of the Bernstein operator on any finite interval
- Some non-unique fixed point theorems of Ćirić type using rational-type contractive conditions
- On some properties of summability methods with variable order
- On the absolute convergence of Fourier series with respect to general orthonormal systems
Articles in the same Issue
- Frontmatter
- Impulsive differential inclusions via variational method
- Frame properties of a part of an exponential system with degenerate coefficients in Hardy classes
- A note on two-variable Chebyshev polynomials
- Spectral analysis of dissipative fractional Sturm–Liouville operators
- Common best proximity pairs in strictly convex Banach spaces
- Traces of Muckenhoupt weighted function spaces in case of distant singularities
- The commutativity of prime Γ-rings with generalized skew derivations
- Δμ-sets and ∇μ-sets in generalized topological spaces
- On strong well-posedness of initial-boundary value problems for higher order nonlinear hyperbolic equations with two independent variables
- Area properties associated with a convex plane curve
- Almost semi-correspondence
- The generalization of the Bernstein operator on any finite interval
- Some non-unique fixed point theorems of Ćirić type using rational-type contractive conditions
- On some properties of summability methods with variable order
- On the absolute convergence of Fourier series with respect to general orthonormal systems
