On the resolvent and spectral functions of a second order differential operator with a regular singularity

Abstract

We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers of $\lambda$ which depend on the singularity. The consequences for the pole structure of the $\zeta$-function, and the small-$t$ asymptotic expansion of the heat-kernel, are also discussed.

LaTeX, 26 pages, 2 figures. Typos corrected

References in corpus (1)

• Global Theory of Quantum Boundary Conditions and Topology Change

Cited by in corpus (17)

• On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry
• Self-adjoint extensions and spectral analysis in Calogero problem
• Potentials in N=4 superconformal mechanics
• Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics
• What is the boundary condition for radial wave function of the Schrödinger equation ?
• The very unusual properties of the resolvent, heat kernel, and zeta function for the operator $-d^2/d{r}^2-1/(4r^2)$
• Scalar Field Probes of Power-Law Space-Time Singularities
• Atom capture by nanotube and scaling anomaly
• Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• The ubiquitous $\zeta$-function and some of its "usual" and "unusual" meromorphic properties
• A New Example of the Effects of a Singular Background on the Zeta Function
• Spectral functions of non essentially selfadjoint operators
• Spectral Functions of Singular Operators
• Krein's Formula And Heat-Kernel Expansion For Some Differential Operators With A Regular Singularity
• Resolvents of cone pseudodifferential operators, asymptotic expansions and applications
• Trace expansions for elliptic cone operators with stationary domains