RT Journal Article ID 61d68a7d59bda613 A1 Chumachenko, V. P. T1 ON LINEAR INDEPENDENCE OF SOME FUNCTION SYSTEMS APPEARING IN THE THEORY OF PLANE WAVE FIELDS JF Telecommunications and Radio Engineering JO TRE YR 2015 FD 2015-05-01 VO 74 IS 4 SP 281 OP 296 K1 linear independence K1 domain-product technique K1 waveguide discontinuities AB 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. PB Begell House LK https://www.dl.begellhouse.com/journals/0632a9d54950b268,30b42b7d71e09a70,61d68a7d59bda613.html