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# Journal of Operator Theory

Volume 50, Issue 2, Fall 2003  pp. 249-261.

An intrinsic difficulty with interpolation on the bidisk

Authors James P. Solazzo
Author institution: Department of Mathematics, University of Georgia, Athens, GA 30602, USA

Summary:  The set of possible values $(w_1,\ldots,w_k)=(f(x_1),\ldots,f(x_k))$ arising from restricting contractive elements $f$ from some uniform algebra $A$ to a finite set $\{ x_1,\ldots,x_k \}$ in the domain is called an interpolation body. When the uniform algebra is the bidisk algebra, Cole and Wermer show that the associated interpolation body is a semi-algebraic set and it is in this sense that the interpolation body is computable''. Motivated by the work of Cole and Wermer, Paulsen introduced the notion of the Schur ideal which acts a natural dual'' object for these interpolation bodies. From this duality'' a stronger notion of computability'' follows which will allow us to discuss the intrinsic differences between interpolation on the bidisk and interpolation on the disk.

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