Smoothness conditions for functions of two variables
-
Omar Dzagnidze
Abstract
In this paper, necessary, sufficient, and necessary and sufficient conditions are given for the smoothness of functions of two variables.
References
[1] N. K. Bary, A Treatise on Trigonometric Series. Vol. I, II, The Macmillan, New York, 1964. Search in Google Scholar
[2] O. Dzagnidze, The smoothness of functions of two variables and double trigonometric series, Real Anal. Exchange 34 (2009), no. 2, 451–470. 10.14321/realanalexch.34.2.0451Search in Google Scholar
[3] O. Dzagnidze, One-dimensional Fourier series of a function of many variables, Trans. A. Razmadze Math. Inst. 171 (2017), no. 2, 167–170. 10.1016/j.trmi.2017.03.001Search in Google Scholar
[4] G. F. B. Riemann, Collected Works (in Russian), Gos. Izd. Tehniko-Teoretich. Literaturi, Moscow, 1948. Search in Google Scholar
[5] A. Zygmund, Smooth functions, Duke Math. J. 12 (1945), 47–76. 10.1215/S0012-7094-45-01206-3Search in Google Scholar
[6] A. Zygmund, Trigonometric Series Vol. I., 2nd ed., Cambridge University, New York, 1959. Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Oscillation of even-order neutral differential equations with retarded and advanced arguments
- Existence and uniqueness of positive solutions for nonlinear fractional mixed problems
- Smoothness conditions for functions of two variables
- Duality pairs induced by Auslander and Bass classes
- Integral transforms and probability distributions involving a generalized hypergeometric function
- Homotopy invariance of the cyclic homology of A ∞-algebras under homotopy equivalences of A ∞-algebras
- On the extreme values of M/M/m queueing systems
- Some properties of the Hermite polynomials
- m-potent commutators of skew derivations on Lie ideals
- Banach spaces of absolutely k-summable series
- On the induced matching problem in hamiltonian bipartite graphs
- Hypercyclicity, supercyclicity, and cyclicity of a weighted composition operator on ℓ p spaces
- Algebraic approach to univariate polynomial derivation
- Free interpolation for the Zygmund class
Articles in the same Issue
- Frontmatter
- Oscillation of even-order neutral differential equations with retarded and advanced arguments
- Existence and uniqueness of positive solutions for nonlinear fractional mixed problems
- Smoothness conditions for functions of two variables
- Duality pairs induced by Auslander and Bass classes
- Integral transforms and probability distributions involving a generalized hypergeometric function
- Homotopy invariance of the cyclic homology of A ∞-algebras under homotopy equivalences of A ∞-algebras
- On the extreme values of M/M/m queueing systems
- Some properties of the Hermite polynomials
- m-potent commutators of skew derivations on Lie ideals
- Banach spaces of absolutely k-summable series
- On the induced matching problem in hamiltonian bipartite graphs
- Hypercyclicity, supercyclicity, and cyclicity of a weighted composition operator on ℓ p spaces
- Algebraic approach to univariate polynomial derivation
- Free interpolation for the Zygmund class
