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13. Understanding properties of extremal Blaschke products

Understanding properties of extremal Blaschke products $B_A$ associated with a matrix $A$ (I propose to call them Crouzeix’s Blaschke products):

Specifically designed numericall experiments may help to investigate these problems.


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      Problem 13.1.

      [E. Wegert] Why do they so often have a low degree?


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          Problem 13.2.

          [E. Wegert] What does a low (or high) degree tell us about the matrix?


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              Problem 13.3.

              [E. Wegert] What are geometric properties of the sub-classes $A\in\mathbb{C}^{d\times d}$ with $\mathrm{deg}\,B_A=k$, $k=0,\ldots,d$?


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                  Problem 13.4.

                  [E. Wegert] Are there relations between the Blaschke product $b$ generating a compression $S_b$ of the shift (Pamela Gorkin’s talk) and its (extremal) Crouzeix Blaschke product $B$?

                      Cite this as: AimPL: Crouzeix's conjecture, available at http://aimpl.org/crouzeix.