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Dispersive estimates and evolution
Organize the independent exterior resolvent, smoothing and Strichartz inputs with their dimensional, exponent and derivative-loss limits, then the negative-scale, causal L1 and real-linear perturbation transfers used by the article.
1 · Prerequisites
- Bounded real-linear perturbations preserve solution estimates
- Homogeneous bounds transfer to L1 retarded forcing
- Endpoint multiplier bounds extended to negative spectral orders
- Exterior Dirichlet realization, H² domain and form domain
- Positive spectral Hilbert scale: duality and interpolation
- The Axiom of Choice
- Integer-order Sobolev spaces and their norms
- Strongly measurable Banach-valued function
- Exterior and truncated obstacle domains
- Non-trapping obstacle
- Dirichlet spectral Sobolev scale and duality
- Nontrapping cutoff resolvent estimates
- Unbounded Borel functional calculus: domains, products, spectral mapping
- Explicit compactly supported smooth cutoffs
- Resolvent and spectrum of an unbounded operator
2 · Logical flowchart
Arrows show item dependencies. A grouped prerequisite node points to items that use one or more of its members; their exact links are listed above.
3 · Items
Lemma
Energy dispersive bounds under bounded trajectory perturbations
Lemma