Asymptotics of the number of the interior transmission eigenvalues

作者：Petkov Vesselin^*; Vodev Georgi

来源：Journal of Spectral Theory, 2017, 7(1): 1-31.

DOI：10.4171/JST/154

• Interior transmission eigenvalues
• Weyl formula with remainder
• eigenvalue-free regions

We prove Weyl asymptotics N(r) = cr(d) + O-epsilon(rd-kappa+epsilon) for all 0 < epsilon << 1, for the counting function N(r) = #{lambda(j) is an element of C \ {0}:vertical bar lambda(j)vertical bar <= r(2)}, r > 1, of the interior transmission eigenvalues (ITE), lambda(j). Here d >= 2 denotes the space dimension and 0 < kappa <= 1 is such that there are no (ITE) in the region {lambda is an element of C: vertical bar Im lambda vertical bar >= C(vertical bar Re lambda vertical bar+1)(1-kappa/2)} for some C > 0.

• 出版日期2017