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Periodic Functions

  • Hua Loo Keng
  • Wang Yuan
Chapter

Abstract

The G s may be regarded as tori. The 1-dimensional torus G1 may be obtained by identifying two end-points of the unit interval 0 ≤ x1 ≤ 1 and G2 by indentifying 2 opposite sides of the unit square 0 ≤ x1 ≤ 1, 0 ≤ x2 ≤ 1. In general, Gs is obtained by identifying the 2s opposite surfaces of the s-dimensional unit cube, i.e., the points
$$ \left( {{x_1},...,{x_{v - 1}},0,{x_{v + 1}},...,{x_s}} \right) $$
and
$$ \left( {{x_1},...,{x_{v - 1}},1,{x_{v + 1}},...,{x_s}} \right) $$
are identified, where 1 ≤ vs.

Keywords

Periodic Function Bounded Variation Quadrature Formula Unit Interval Integral Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Science Press. Beijing 1981

Authors and Affiliations

  • Hua Loo Keng
    • 1
  • Wang Yuan
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingThe People’s Republic of China

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