Index
Fractal uncertainty and quantum chaos knowl batch
Dependency-ordered index of atomic knowls supporting Alex Cohen's higher-dimensional fractal uncertainty paper.
Core idea
This index organizes the new axiomatic knowls supporting the paper Fractal uncertainty in higher dimensions. It begins with geometric and analytic prerequisites, follows the Beurling–Malliavin proof chain, and ends with the fractal-uncertainty theorem and its quantum-chaos application. Existing corpus knowls are linked in the dependency notes rather than duplicated here.
Quantitative geometry and notation
Fourier and potential-theoretic foundations
- Bounded Fourier support
- Paley–Wiener theorem for bounded Fourier support
- Hilbert transform
- Poisson kernel of the upper half-plane
- Poisson extension to the upper half-plane
- Dirichlet-to-Neumann operator on the upper half-plane
- X-ray transform
- Oscillatory integral
- Harmonic function
- Maximum principle for harmonic functions
- Upper-semicontinuous function
- Subharmonic function
- Subharmonicity of the logarithmic modulus
- Entire function of several complex variables
- Levi form of a function
- Plurisubharmonic function
- Strictly plurisubharmonic function
- Hörmander L2 theorem for the d-bar equation
- Holomorphic L2 mean-value estimate
Beurling–Malliavin chain
- Beurling–Malliavin multiplier theorem
- Radial-line growth functional of a weight
- Linewise Poisson extension operator
- Exact plurisubharmonic Beurling–Malliavin extension
- Plurisubharmonic Beurling–Malliavin proposition
- Analytic Beurling–Malliavin proposition
- Higher-dimensional Beurling–Malliavin multiplier theorem
Fractal uncertainty chain
Quantum-chaos application
Reused prerequisite knowls
The batch reuses existing records for the Fourier transform on Schwartz space, Fourier inversion, Plancherel's theorem, spaces, Lebesgue measure and integration, distributions and distributional derivatives, support and indicator functions, Hessians, Lipschitz continuity, bump functions, orthogonal complements, positive-semidefinite matrices, Dolbeault operators, and the Laplace–Beltrami operator. Those records remain their canonical owners.
References
- Alex Cohen, “Fractal uncertainty in higher dimensions,” 2024. arXiv record.