 Quarter-plane oblique boundary spectral functions

ID: quarter-plane-oblique-boundary-spectral-functions

q

, prescribe

- sin β_{1} q_{x} + cos β_{1} q_{y} = h_{1}

on the vertical axis and

cos β_{2} q_{x} - sin β_{2} q_{y} = h_{2}

on the horizontal axis. Their orthogonal derivatives

j_{1}, j_{2}

determine the missing gradient components. If

H_{1}, J_{1}

use the kernel

e^{k y}

and

H_{2}, J_{2}

use

e^{- ik x}

, the clockwise spectra

q_{1} = \int_{0}^{i \infty} e^{- ik z} q_{z} d z

q_{2} = - \int_{0}^{\infty} e^{- ik z} q_{z} d z

have the displayed expressions. Their global relation is

q_{1} + q_{2} = 0

in the third spectral quadrant.

// Target: analysis.bigb

 New to topics? Read the docs here!