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 Δ*u* + *χ*^{2}u = 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 *χ*^{2} with the accumulation point at infinity. For rectangle and arbitrary triangle these values have been found analytically.
PB Begell House
LK http://dl.begellhouse.com/journals/0632a9d54950b268,30b42b7d71e09a70,61d68a7d59bda613.html