2023/09/04 by Yash Rastogi, Rastogi, Yash
Engineering · Mathematics · #46E22 #47B35 #65L20 #65M12 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2309.01759
openalex publication_date 2023/09/04 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28
The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent condition of Kreiss-Ritt type. Furthermore, we show that the power bound is bounded above by a polynomial of the resolvent condition. The operators under investigation do not fall into a well-understood class, so our analysis utilizes explicit reproducing kernel techniques. Our methods apply mutatis mutandis to composites of Toeplitz operators with polynomial symbol, which arise frequently in the numerical solution of initial value problems encountered in science and engineering.