Telecommunications and Radio Engineering

ON LINEAR INDEPENDENCE OF SOME FUNCTION SYSTEMS APPEARING IN THE THEORY OF PLANE WAVE FIELDS

ABSTRAKT

In the paper the linear independence conditions are analyzed for infinite systems of functions which are used in the frame of the domain-product technique for a wave field representation in the domains confined by convex polygons. The domain is regarded as a common part of overlapping half-planes. The sought for field component satisfying the equation Δu + χ²u = 0 is represented as a superposition of expansions defined on the half-planes which allow separation of variables in local coordinates. It is shown that the arising overall system of functions, in terms of which the expansion is performed, is linearly independent except for the greatest term of the countable set of spectral parameter magnitudes χ² with the accumulation point at infinity. For rectangle and arbitrary triangle these values have been found analytically.