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Finite rank multivariable Hankel forms

✍ Scribed by S.C. Power


Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
408 KB
Volume
48
Category
Article
ISSN
0024-3795

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We give a different proof of Power'.,; several variables generalization o[" the wellknown Kronecker's result on tinitc rank Hankel matrices. This also leads to ~,, formula for the rank of a small Hankel operator on polydisk in terms of a certain degree of its rational symbol. ~.

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Let H be an inÿnite Hankel matrix with hi+j-2 as its (i; j)-entry, h k = n l=1 r l z k l , k = 0; 1; : : : ; |z l | ‘ 1, and r l ; z l ∈ C. We derive upper bounds for the 2-condition number of H as functions of n, r l and z l , which show that the Hankel matrix H becomes well conditioned whenever th