Convergence, Uniqueness, and Summability of Multiple Trigonometric Series

DOI10.2307/1995730zbMath0233.42014OpenAlexW4240851849MaRDI QIDQ5641586

J. Marshall Ash, Grant V. Welland

Publication date: 1972

Full work available at URL: https://doi.org/10.2307/1995730

Mathematics Subject Classification ID

Multipliers for harmonic analysis in several variables (42B15) Convergence and divergence of series and sequences (40A05) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Summability in several variables (42B08) Summability and absolute summability of Fourier and trigonometric series (42A24) Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces (42-02)

Related Items (24)

Victor Shapiro and the Theory of Uniqueness for Multiple Trigonometric Series ⋮ On uniqueness of the additive segment functions and trigonometric series ⋮ Unnamed Item ⋮ Generalizations of the Wave Equation ⋮ Fourier-Laplace series on a sphere ⋮ Countably multiple null series ⋮ A Cantor-Lebesgue theorem with variable “coefficients” ⋮ A uniqueness theorem for entire functions of two complex variables ⋮ Rectangular summation of multiple Fourier series and multi-parametric capacity ⋮ The billard theorem for multiple random Fourier series ⋮ Coefficients of convergent multiple Haar series ⋮ Polynomial inequalities on measurable sets and their applications ⋮ Uniqueness sets for multiple Haar series ⋮ A uniqueness theorem for multiple lacunary trigonometric series ⋮ The Cantor-Lebesgue and Denjoy-Luzin properties for double systems of functions ⋮ On the strong Cesàro summability of double orthogonal expansions ⋮ Convergence and Divergence of Series Conjugate to a Convergent Multiple Fourier Series ⋮ Uniqueness theorems for simple trigonometric series with application to multiple series ⋮ Multiple Fourier series and integrals ⋮ Cantor-Lebesgue theorem for double trigonometric series ⋮ One and two dimensional Cantor-Lebesgue type theorems ⋮ Boundedness of convergent mean multiple functional series ⋮ Integrability theorem of multiple trigonometric series ⋮ Trigonometric integrals and pseudofunctions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiple trigonometric series of a particular type
• On convergence and growth of partial sums of Fourier series
• Convergence almost everywhere of certain singular integrals and multiple Fourier series
• Some theorems on double trigonometric series
• On the differentiability of multiple integrals
• The Approximate Divergence Operator
• On the divergence of multiple Fourier series
• A Cantor-Lebesgue Theorem in Two Dimensions
• On the convergence of multiple Fourier series
• Fourier series in several variables
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
• Uniqueness of multiple trigonometric series

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