Analog of Dirichlet multidimensional discontinuous factor for Riesz means in complex domain (Q1091594)

Let \(\{\Lambda_ k\}\) be a sequence of complex numbers, Re \(\Lambda\) \({}_ k\geq 0\), \(| Im \Lambda_ k| \leq C_ 1=const\), and let \(\nu\geq -\), \(\alpha >-1\), \(\lambda\geq 1\). The author investigates an analog of the multidimensional discontinuous Dirichlet factor for Riesz means \[ \int^{R}_{0}J_{\nu +1+\alpha}(r\Lambda)J_{\nu}(r\Lambda_ k)r^{-\alpha}dr \] which arises under the expanding of a non selfadjoint extension of the Laplace operator into eigen and adjoined functions.