Definition:Lipschitz Seminorm
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Definition
Let $\struct {X_\mathbf A, \sigma_\mathbf A}$ be a shift of finite type.
Let $\theta \in \openint 0 1$.
Let $\map {F_\theta} {X_\mathbf A}$ be the Lipschitz space on $X_\mathbf A$.
The Lipschitz seminorm of $f \in \map {F_\theta} {X_\mathbf A}$ is defined as:
- $\ds \size f_\theta := \sup_{n \mathop \in \N} \dfrac {\map {\mathrm {var}_n} f} {\theta ^n}$
Also see
Source of Name
This entry was named for Rudolf Otto Sigismund Lipschitz.
Sources
- 1990: William Parry and Mark Pollicott: Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics: Chapter $1$: Subshifts of Finite Type and Function Spaces