{"paper":{"title":"Nonlinear bang-bang eigenproblems and optimization of resonances in layered cavities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.SP","physics.optics"],"primary_cat":"math.OC","authors_text":"Ievgen V. Verbytskyi, Illya M. Karabash, Olga M. Logachova","submitted_at":"2015-08-19T17:08:38Z","abstract_excerpt":"Quasi-normal-eigenvalue optimization is studied under constraints $b_1(x) \\le B(x) \\le b_2 (x)$ on structure functions $B$ of 2-side open optical or mechanical resonators. We prove existence of various optimizers and provide an example when different structures generate the same optimal quasi-(normal-)eigenvalue. To show that quasi-eigenvalues locally optimal in various senses are in the spectrum $\\Sigma^{nl}$ of the bang-bang eigenproblem $y\" = - \\omega^2 y [ b_1 + (b_2 - b_1) \\chi_{\\mathbb{C}_+} (y^2 ) ]$, where $\\chi_{\\mathbb{C}_+} (\\cdot)$ is the indicator function of the upper complex hal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04706","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}