ON THE INDEX AND SPECTRUM OF INTEGRAL OPERATORS OF POTENTIAL TYPE ALONG RADON CURVES

摘要: A study is made of how classical integral equations mathematical physics are affected by nonregularity the contour integration. criterion obtained for a matrix equation with operator potential type acting in to be Noetherian, and index computed. It established that an corresponding interior Dirichlet problem harmonic functions Noetherian all except finite or countable number values determined angles contour; defect numbers, which depend on mentioned, found. Analogous results system planar theory elasticity. The non-Noetherian spectrum space continuous vector-valued described. This result illustrated example elasticity (for which, particular, Fredholm radius found) direct value double layer potential.