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A Hardy-Davies-Petersen Inequality for a Class of Matrices

Published online by Cambridge University Press:  20 November 2018

P. D. Johnson Jr.  and
R. N. Mohapatra
P. D. Johnson Jr.
Affiliation:
American University of Beirut, Beirut, Lebanon
R. N. Mohapatra
Affiliation:
University of Alberta, Edmonton, Alberta
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Let ω be the set of all real sequences a = ﹛an﹜n ≧0. Unless otherwise indicated operations on sequences will be coordinatewise. If any component of a has the entry oo the corresponding component of a-1 has entry zero. The convolution of two sequences s and q is given by s * q. The Toeplitz martix associated with sequence s is the lower triangular matrix defined by tnk = sn-k (n ≧ k), tnk = 0 (n < k). It can be seen that Ts(q) = s * q for each sequence q and that Ts is invertible if and only if s0 ≠ 0. We shall denote a diagonal matrix with diagonal sequence s by Ds.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 458 - 465
Copyright
Copyright © Canadian Mathematical Society 1978

References

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