Abstract

The spectral function Θ( t) = ∑ j = 1 ∞ exp(− tλ j ), where { λ j } j = 1 ∞ are the eigenvalues of the Laplace operator Δ = ∑ i = 1 2 ( ∂ ∂x i ) 2 in the x 1 x 2-plane, is studied for a general convex domain together with an impedance condition on a part of its boundary and another impedance condition on the remaining part of that boundary.

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