 Semistrip Laplace spectral global relation

ID: semistrip-laplace-spectral-global-relation

Let

q

be a real harmonic function in a semistrip,

g_{0} (x) = q (x, 0)

g_{l} (x) = q (x, l)

and

h (y) = q (0, y)

. Let

G_{j}, N_{j}

be the negative-exponential Half-range Fourier transforms of

g_{j}

and

q_{y} (x, j)

, and put

H (k) = \int_{0}^{l} e^{k y} h (y) d y

W (k) = \int_{0}^{l} e^{k y} q_{x} (0, y) d y

e^{- ik z} q_{z} d z

has zero boundary integral. Integration by parts of tangential derivatives cancels all corner values and gives the displayed global relation, for

Im k \leq 0

// Target: analysis.bigb

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