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Notes on the Unconditional Convergence of Multidimensional Functional Series

Published/Copyright: February 18, 2010
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Georgian Mathematical Journal
From the journal Volume 7 Issue 2

Abstract

The convergence of a multidimensional functional series essentially depends on the way its partial sums are formed. Different ways of definition of partial sums lead to different kinds of convergence. In the paper relations between various kinds of unconditional almost everywhere convergence of multidimensional functional series are studied.

Key words and phrases:: Multidimensional series; unconditional convergence
Received: 1999-04-14
Published Online: 2010-02-18
Published in Print: 2000-June

© Heldermann Verlag

Articles in the same Issue

  1. On the Oscillation of Certain Second Order Differential Equations
  2. Notes on the Unconditional Convergence of Multidimensional Functional Series
  3. Existence of Mild Solutions of Semilinear Evolution Inclusions with Nonlocal Conditions
  4. Interface Crack Problem for Electroelastic Body
  5. K-Convexity and Duality for Almost Summing Operators
  6. On the Dynamics of the Generalized Emden–Fowler Equation
  7. On the Maximal Functions of the Class L(Rn) \ L(1 + ln+L)(Rn)
  8. nth Order Neutral Differential Equations with Properties Aw and Bw
  9. On Second Order Nonlinear Equations with Rectilinear Characteristics
  10. Nonuniqueness Theorem for a Singular Cauchy Problem
  11. On Oscillation and Nonoscillation of a Second Order Half-Linear Equation
  12. Oscillation of Higher Order Delay Differential Equations of Neutral Type
  13. Summation of Singular Series Corresponding to the Representation of Integers by Some Quadratic Forms in Fourteen Variables
  14. Monotone Iterative Techniques and a Periodic Boundary Value Problem for First Order Differential Equations with a Functional Argument
  15. Expected Number of Real Zeros of Lévy and Harmonizable Stable Random Polynomials
  16. Generalized Derivatives of an Arbitrary Order and the Boundary Properties of Differentiated Poisson Integrals for the Half-Space
https://doi.org/10.1515/GMJ.2000.215
Keywords for this article
Multidimensional series; unconditional convergence

Articles in the same Issue

  1. On the Oscillation of Certain Second Order Differential Equations
  2. Notes on the Unconditional Convergence of Multidimensional Functional Series
  3. Existence of Mild Solutions of Semilinear Evolution Inclusions with Nonlocal Conditions
  4. Interface Crack Problem for Electroelastic Body
  5. K-Convexity and Duality for Almost Summing Operators
  6. On the Dynamics of the Generalized Emden–Fowler Equation
  7. On the Maximal Functions of the Class L(Rn) \ L(1 + ln+L)(Rn)
  8. nth Order Neutral Differential Equations with Properties Aw and Bw
  9. On Second Order Nonlinear Equations with Rectilinear Characteristics
  10. Nonuniqueness Theorem for a Singular Cauchy Problem
  11. On Oscillation and Nonoscillation of a Second Order Half-Linear Equation
  12. Oscillation of Higher Order Delay Differential Equations of Neutral Type
  13. Summation of Singular Series Corresponding to the Representation of Integers by Some Quadratic Forms in Fourteen Variables
  14. Monotone Iterative Techniques and a Periodic Boundary Value Problem for First Order Differential Equations with a Functional Argument
  15. Expected Number of Real Zeros of Lévy and Harmonizable Stable Random Polynomials
  16. Generalized Derivatives of an Arbitrary Order and the Boundary Properties of Differentiated Poisson Integrals for the Half-Space
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