Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

23 papers
Browse papers
  1. RH: Complete Signed Certificates and Canonical Null SynthesisScott SchubrEdition 12 · 2026-11-01 Public
  2. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 4 · 2026-11-01 Public
  3. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 5 · 2026-11-01 Public
  4. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 2 · 2026-10-31 Public
  5. Positive Operator Cocycles in Shrinking CorridorsScott SchubrEdition 2 · 2026-10-31 Public
  6. Spectral escape for interacting and coalescing signed potential formsScott SchubrEdition 5 · 2026-10-30 Public
  7. Large negative subspaces for positive Euler deformationsScott SchubrEdition 3 · 2026-10-30 Public
  8. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 3 · 2026-10-30 Public
  9. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 4 · 2026-10-30 Public
  10. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  11. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  12. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  13. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  14. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  15. Mean ergodic convergence from near-diagonal subadditivityScott SchubrEdition 2 · 2026-10-27 Public
  16. Quantitative Null-Space Compression for a Weighted Weil OperatorScott SchubrEdition 2 · 2026-10-27 Public
  17. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  18. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  19. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  20. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  21. Sharp regularity criteria for arithmetic cutoff functionalsScott SchubrEdition 1 · 2026-10-26 Public
  22. Optimal energy for Dirichlet repairs in divisor bandsScott SchubrEdition 1 · 2026-10-26 Public
  23. Certified negative-band approximation for odd Weil formsScott SchubrEdition 1 · 2026-10-26 Public
PublicEdition 2

Observation norms under double-exponential confinement

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

We determine the small-regularization norm of a weighted observation of a positive Fourier-energy operator under double-exponential spatial confinement. The leading term is the logarithm of the logarithm of the inverse regularization, with an explicit constant given by the quadratic part of the symbol and a constrained Dirichlet eigenvalue on an interval. Finitely many fixed nonzero polynomial-exponential constraint chains leave this constant unchanged; zero-exponent moment chains survive in the limiting problem. In particular a mean-zero constraint halves the leading observation norm. For the original two-row theta-weighted reference, the result gives the exact constant together with finite explicit bounds. Applications include a full factored-residual covariance enclosure and a complete-arithmetic sandwich bound. The proofs retain the specified compact-core closure and all mixed residual terms.

Read the full paper in the original PDF.