Salimov, Ya. Sh. Analog of Dirichlet multidimensional discontinuous factor for Riesz means in complex domain. (English. Russian original) Zbl 0623.47062 Math. Notes 40, 784-793 (1986); translation from Mat. Zametki 40, No. 4, 492-510 (1986). 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. Reviewer: N.Vasilevski MSC: 47Gxx Integral, integro-differential, and pseudodifferential operators 35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs 47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces Keywords:multidimensional discontinuous Dirichlet factor for Riesz means PDFBibTeX XMLCite \textit{Ya. Sh. Salimov}, Math. Notes 40, 784--793 (1986; Zbl 0623.47062); translation from Mat. Zametki 40, No. 4, 492--510 (1986) Full Text: DOI References: [1] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second Order Differential Equations, Oxford Univ. Press (1962). · Zbl 0099.05201 [2] V. A. Il’in, ?On summability of Fourier series with respect to eigenfunctions by Riesz, Cesaro, and Poisson-Abel means,? Differents. Uravn.,2, No. 6, 816-827 (1966). [3] V. A. Il’in, ?Necessary and sufficient conditions for spectral expansions to be basic and equiconvergent with trigonometric series,? II, Differents. Uravn.,16, No. 6, 980-1009 (1980). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.