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math.FA2026
Dyadic Resolvent Representations of Self-Adjoint Operators: Propagator Expansions, Spectral Measures, and Zeta Functions
Nicholas Castillo
For a self-adjoint operator on a Hilbert space, the dyadic resolvent representation of Castillo, Costin and Costin expresses the resolvent as a series in…
math.HO2026
The Dyadic Cauchy-Kernel Identity: Several Roads Back to Classical Objects
Nicholas Castillo
This is an expository note. We take the dyadic Cauchy-kernel identity of Castillo-Costin-Costin, a global rational/factorial decomposition built on the polylogarithm, and follow it…