Moment Problems and Spectral Functions
Ryan Abbott, William Jay, Patrick Oare
TL;DR
This paper explores the use of Nevanlinna-Pick interpolation and moment problems to establish bounds on spectral functions, emphasizing the role of causality and convexity in the data space.
Contribution
It provides a review of key results in Nevanlinna-Pick interpolation and moment problems, including a simple proof of convexity in causal data space.
Findings
Causal data space in Nevanlinna-Pick interpolation is convex
Provides bounds on spectral functions using analytic structures
Reviews useful results in moment problems
Abstract
Nevanlinna-Pick interpolation and moment problems use the analytic structures provided by causality in order to provide rigorous bounds on smeared spectral functions. This proceedings discusses Nevanlinna-Pick interpolation and moment problems and reviews some useful results, including a simple proof that the space of causal data in Nevanlinna--Pick interpolation is convex.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Holomorphic and Operator Theory · Nonlinear Differential Equations Analysis