4 papers
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…
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…
Approximations of Functions With Essential Singularities with Applications to Painlevé's First Transcendent
Nicholas Castillo
In this work we develop an algorithmic procedure for associating a function defined on the Riemann surface of the to given asymptotic data from a function at an essential si…
On the pointwise existence of Cauchy integrals
Nicholas Castillo, Ovidiu Costin, Kriti Sehgal
The Riemann-Hilbert (RH) approach, whose origins can be traced back to Riemann's PhD thesis, is well known to be far-reaching. It provides a general framework for expressing soluti…