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The conversion of resolvent conditions into semigroup estimates is crucial inthe stability analysis of hyperbolic partial differential equations. For twofamilies of multiple Toeplitz operators, we relate the power bound with aresolvent condition of Kreiss-Ritt type. Furthermore, we show that the powerbound is bounded above by a polynomial of the resolvent condition. Theoperators under investigation do not fall into a well-understood class, so ouranalysis utilizes explicit reproducing kernel techniques. Our methods apply\textit{mutatis mutandis} to composites of Toeplitz operators with polynomialsymbol, which arise frequently in the numerical solution of initial valueproblems encountered in science and engineering.

Extremal Growth of Multiple Toeplitz Operators and Applications to Numerical Stability of Approximation Schemes