Triangular summation method
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.
|||G.H. Hardy, "Divergent series" , Clarendon Press (1949)|
|||R.G. Cooke, "Infinite matrices and sequence spaces" , Macmillan (1950)|
|||S.A. Baron, "Introduction to the theory of summability of series" , Tartu (1966) (In Russian)|
Triangular summation method. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Triangular_summation_method&oldid=15775