RH Toolkit 1: Deferral Operators on ℓ² and Their Continuous Realization

This toolkit establishes the foundational operator-theoretic framework for the RH Toolkit program. It defines a class of admissible deferral kernels on discrete Hilbert sequence spaces and proves their boundedness, compactness, Hilbert–Schmidt property, and (when symmetric) self-adjointness. The associated spectral decomposition is developed in full generality. A discrete-to-continuous transfer principle is then constructed, realizing these operators as integral operators on suitable continuous function spaces. This discrete–continuous bridge provides the analytic foundation required for heat-kernel methods, spectral zeta functions, and completed determinants in later toolkits. No number-theoretic or zeta-theoretic assumptions are made.