The very unusual properties of the resolvent, heat kernel, and zeta function for the operator −d2∕dr2−1∕(4r2)

DOI10.1063/1.2189194zbMath1111.58025arXivmath-ph/0511002OpenAlexW3099888766MaRDI QIDQ3441747

Jinsung Park, Klaus Kirsten, Paul Loya

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0511002

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Linear symmetric and selfadjoint operators (unbounded) (47B25) Determinants and determinant bundles, analytic torsion (58J52) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (13)

Heat-kernel expansion on noncompact domains and a generalized zeta-function regularization procedure ⋮ Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators ⋮ Zeta Functions of Elliptic Cone Operators ⋮ On self-adjoint boundary conditions for singular Sturm-Liouville operators bounded from below ⋮ Regular singular Sturm-Liouville operators and their zeta-determinants ⋮ The exotic heat-trace asymptotics of a regular-singular operator revisited ⋮ The three-dimensional \(O(n)\) \(\varphi^4\) model on a strip with free boundary conditions: exact results for a nontrivial dimensional crossover in the limit \(n\to\infty\) ⋮ Trace expansions for elliptic cone operators with stationary domains ⋮ Explicit Krein resolvent identities for singular Sturm-Liouville operators with applications to Bessel operators ⋮ Spectral functions for the Schrödinger operator on R+ with a singular potential ⋮ Zeta determinant for Laplace operators on Riemann caps ⋮ A new example of the effects of a singular background on the zeta function ^* ⋮ Heat-trace asymptotics for edge Laplacians with algebraic boundary conditions

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