Bochner integral norm inequality

Depends on

• Bochner integrability criterion
• The Banach-valued simple integral is well defined
• Additivity of the nonnegative Lebesgue integral
• Monotonicity and nonnegative homogeneity of the nonnegative integral

Used by

• A semigroup with unbounded generator is not norm continuous at zero Corollary
• Abstract parabolic smoothing for mild solutions Corollary
• Parseval and Fourier inversion for compact groups Corollary
• Resolvent power estimates for semigroup generators Corollary
• Spatial smoothing of forcing separated from the observation time Corollary
• Infinitely many modes admit inequivalent irreducible regular Weyl representations Counterexample
• The translation semigroup is not analytic Counterexample
• Compact-group isotypic projection Definition
• The Duhamel heat potential Definition
• Bochner integral of a countably valued function Example
• A Bochner density defines an absolutely continuous vector measure Lemma
• A Lipschitz Fréchet derivative gives a quadratic linearization remainder Lemma
• A positive rank-one Haar average is a nonzero compact intertwiner Lemma
• A system of imprimitivity integrates to a nondegenerate representation of the transformation algebra Lemma
• Analytic Duhamel cancellation removes the generator singularity Lemma
• Anchored IRGNM error identity and fixed-reference residual inequality Lemma
• Average convergence for a continuous Banach-valued function Lemma
• Characters of the L1 algebra of an abelian group Lemma
• Fundamental theorem of calculus for Banach-valued continuous curves Lemma
• Integrated pressure recovery and MINI pressure-primitive convergence Lemma
• Laplace resolvents of a unitary group Lemma
• Long-run covariance of an L2-m-approximable shift is trace class Lemma
• Nondentability produces a vector measure without density Lemma
• Partial one-homogeneous energy is continuous under W2 convergence Lemma
• Primitive and Cauchy theorem for Banach-valued holomorphic maps on star-shaped domains Lemma
• Recovering a unitary group representation from a nondegenerate L one representation Lemma
• Smooth and K-finite vectors are dense and stable under the derived action Lemma
• Smooth mollifiers approximate Bochner L² functions Lemma
• Spectral measure of a unitary representation of an abelian group, covariance, and ergodicity Lemma
• Taylor expansion with integral remainder for Banach-valued curves Lemma
• The Dunford contour construction satisfies the semigroup law and strong continuity at the vertex Lemma
• The Dunford contour integral defines a bounded holomorphic family on the sector Lemma
• The Gaussian Weyl average is a rank-one projection Lemma
• The generator of a unitary group is closed and skew-adjoint Lemma
• The L1 action of a strongly continuous unitary representation Lemma
• The variation-of-constants integral is continuous for integrable forcing Lemma
• Time integrals of semigroup orbits lie in the generator domain Lemma
• Time mollification preserves the evolution-space derivative Lemma
• Time translations and mollification in Bochner Lp Lemma
• Weighted overlapping-block moment and covariance limits Lemma

…and 16 more results.

Dependency tree · two levels

16 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Gerald Teschl, Topics in Real and Functional Analysis (standard reference, not scraped)