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A generalization of Rudin's multivariable stability theorem

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2 Author(s)
Hertz, D. ; Technion-Israel Insitute of Technology, Haifa, Israel ; Zeheb, E.

Rudin's N-variable stability theorem requires testing, in addition to a multidimensional condition on the distinguished boundary, a single one-variable condition. A generalization of Rudin's theorem is presented in this paper, in which the single-variable condition is replaced with n single-variable conditions where 1 \leq n \leq N at one's choice. The tradeoff is between simpler and a smaller number of single-variable conditions. The special case n = 1 reduces to the original Rudin theorem. Other special cases reduce to some well-known stability theorems, either with 1 or with N single-variable conditions. An example is provided where choosing n \neq 1 , N is advantageous from the computational point of view.

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:33 ,  Issue: 3 )