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  1. Spectral Crowding and Compression Limits for Arithmetic Covariance OperatorsScott SchubrEdition 2 · 2026-11-02 Public
  2. Positive Operator Cocycles in Shrinking CorridorsScott SchubrEdition 2 · 2026-10-31 Public
  3. Spectral escape for interacting and coalescing signed potential formsScott SchubrEdition 5 · 2026-10-30 Public
  4. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 3 · 2026-10-30 Public
  5. Relative tail payment and spectral enclosuresScott SchubrEdition 1 · 2026-10-29 Public
  6. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  7. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  8. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  9. Critical-tail localization and growing theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  10. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

Observation norms under double-exponential confinement

Scott Schubr

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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.

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