English

Functional determinants for the second variation

Functional Analysis 2022-12-29 v1 Classical Analysis and ODEs

Abstract

We study the determinant of the second variation of an optimal control problem for general boundary conditions. Generically, this operators are not trace class and the determinant is defined as a principal value limit. We provide a formula to compute this determinant in terms of the linearisation of the extremal flow. We illustrate the procedure in some special cases, proving some Hill-type formulas.

Keywords

Cite

@article{arxiv.2212.13455,
  title  = {Functional determinants for the second variation},
  author = {Stefano Baranzini},
  journal= {arXiv preprint arXiv:2212.13455},
  year   = {2022}
}

Comments

41 pages

R2 v1 2026-06-28T07:53:50.520Z