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In this article we analyze the spectral zeta function, the heat kernel, and the resolvent of the operator −d2/dr2+κ/r2+r2 over the interval (0,∞) for κ≥−1/4. Depending on the self-adjoint extension chosen, nonstandard properties of the zeta function and of asymptotic properties of the heat kernel and resolvent are observed. In particular, for the zeta function nonstandard locations of poles as well as logarithmic branch cuts at s=−k, k∊N0, do occur. This implies that the small-t asymptotic expansion of the heat kernel can have nonstandard powers as well as terms such as tk/(ln t)l+1 for k,l∊N0. The corresponding statements for the resolvent are also shown. Furthermore, we evaluate the zeta determinant of the operator for all values of κ and any self-adjoint extension.

In this note, we explicitly compute the functional determinant of a Dirac Laplacian with nonlocal pseudodifferential boundary conditions over a finite cylinder in terms of the ζ-function of the Dirac operator on the cross section and the pseudodifferential operators defining the boundary conditions. In particular, this result reduces to our previous formula [J. Phys. AJPHAC5 37, 7381 (2004)] for the special case of generalized Atiyah–Patodi–Singer conditions. To prove our main result, we use the gluing and comparison formulas established by the present authors in Refs 14 and 15.