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The proof was in the Chemin-Lerner space framework (see e.g. [13, 14]).
Many of these results are couched in a Banach space framework and involve bounded orbits.
Wightman's axiomatic QFT has its roots in Schwartz's theory of distributions, and it was later developed in the rigged Hilbert space framework.
Algebraic QFT has its roots in the work of von Neumann on operator algebras, which was developed by him in an attempt to generalize the Hilbert space framework.
In the late 1960s, the axiomatic approach was explicitly put into the rigged Hilbert space framework by Bogoliubov and co-workers.
It was further refined in the late 1960s by Bogoliubov, who explicitly placed axiomatic QFT in the rigged Hilbert space framework (Bogoliubov et al. 1975, p. 256).
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We do so by considering the stochastic log-volatility (SV) state-space framework.
This paper revisits minimum-variance (MV) control design for astronomical AO systems in a state-space framework.
We introduce a state-space framework in which all spatially invariant systems with this property can be characterized.
A scale-space framework describes a noisy image as a stack of progressively evolving many smooth images, each one with their corresponding scale [8].
Motivated by this, we have analyzed the linear DOB in the state-space framework, and have derived a necessary and sufficient condition for robust stability.
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