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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
- The Axiom of Choice
- Banach space
- A bounded linear operator between normed spaces
- Integer-order Sobolev spaces and their norms
- Integer-order Sobolev spaces are Banach
- Strongly measurable Banach-valued function
- Well-defined strip norm and the action of a common endpoint operator
- A single collar-reflection and free-tail exterior extension
- Restriction quotient and Bochner interpolation for the exterior extension
- J. C. Bellido and G. García-Sáez, Bessel Potential Spaces and Complex Interpolation: Continuous embeddings, arXiv:2503.04310v6 · Compatible couples and sums: PDF pp.4–6; §2.2, PDF pp.9–10 (strip definition, Banach property and exact operator bound); Example 2.7(i), PDF p.11 (Bochner interpolation); Definitions 3.1, 3.3, 3.6 and Theorem 3.7, PDF pp.15–17 (whole-space Bessel convention and identity).
- Continuous free convolution on a finite time interval
- Global real evolution, cocycle and inverse
- Bochner variation of constants for real evolution
- Topological vector spaces over the real and complex fields
- Spectral cutoff cores and unitary identifications of completed scales
- Exact scale interpolation and endpoint operator transport
- Lifted spectral measure and isometric Bochner scale interpolation
- Riesz representation for Hilbert spaces
- Flow calculus of a self-adjoint generator: commutation, invariance and differentiability
- Spectral theorem for unbounded self-adjoint operators (PVM form)
- Unbounded Borel functional calculus: domains, products, spectral mapping
- Closed semibounded symmetric forms and their associated operators
- Semibounded closed-form representation and perturbation
- Zero-boundary Sobolev space as a norm closure
- The Sobolev space H¹ is a Hilbert space
- Smooth compactly supported functions of an open set are dense in L²
- Short-interval real Volterra contraction
- A contraction of a nonempty complete metric space into itself has exactly one fixed point, the limit of the iterates from any starting point
- Gronwall's integral inequality with variable and constant coefficients
- Bochner integral norm inequality
- Linearity of the Bochner integral
- Exterior and truncated obstacle domains
- Complex integer-order Sobolev notation
- Dirichlet Laplacian and positive shift
- Exterior Dirichlet realization, H² domain and form domain
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
An explicit common interpolation model for the fractional Strichartz targets
Lemma
Transfer of a compatible spacetime norm through the free forcing map
Lemma
Positive spectral Hilbert scale: duality and interpolation
Lemma
Bounded real-linear perturbations preserve solution estimates
Definition