Functional bounds, series, and log convexity of Rayleigh higher derivatives

The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the plane obtained by stereographic projection of the fundamental domains on an orbifolded two-sphere. Examples treated are the sector of a disk and a circular crescent. The effective action on a spherical cap is also determined.

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Scalar Casimir effect in a circular Aharonov - Bohm quantum billiard

Romeo-i-Val¹

1996

J. Phys. A: Math. Gen.

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Functional bounds, series, and log convexity of Rayleigh higher derivatives

Cited by 5 publications

References 6 publications

The complete monotonicity of the Rayleigh function

The complete monotonicity of the Rayleigh function

Functional determinants on regions of the plane and sphere

Scalar Casimir effect in a circular Aharonov - Bohm quantum billiard

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