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Triangular summation method

From Encyclopedia of Mathematics
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A matrix summation method defined by a triangular matrix

that is, by a matrix for which for . A triangulation summation method is a special case of a row-finite summation method. A triangular matrix is called normal if for all . The transformation

realized by a normal triangular matrix has an inverse:

where is the inverse of . This fact simplifies the proof of a number of theorems for matrix summation methods determined by normal triangular matrices. Related to the triangular summation methods are, e.g., the Cesàro summation methods and the Voronoi summation method.

References

[1] G.H. Hardy, "Divergent series" , Clarendon Press (1949)
[2] R.G. Cooke, "Infinite matrices and sequence spaces" , Macmillan (1950)
[3] S.A. Baron, "Introduction to the theory of summability of series" , Tartu (1966) (In Russian)
How to Cite This Entry:
Triangular summation method. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Triangular_summation_method&oldid=15775
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article