Detecting mass points of representing measures (Q1410497)

The problem of detecting atoms of measures is of great importance. In addition to typical situations, like orthodox moment problems and orthogonal polynomials, one has occurred quite recently, the appearance of discrete measures in Sobolev orthogonality [\textit{W. D. Evans, L. L. Littlejohn, F. Marcellán, C. Markett} and \textit{A. Ronveuax}, SIAM J. Math. Anal. 28, 446--467 (1995; Zbl 0824.33006)]. In this paper, the author discussed a possibility of deciding whether measures representing a moment sequence or realizing orthogonality of polynomials have atoms. This was done on the real line and in several variables. The idea developed here comes from \textit{F. H. Szafraniec} [Ann. Polon. Math. 42, 345--347 (1983; Zbl 0535.41006)] and that in turn is hidden by \textit{D. V. Widder} [The Laplace Transform (Princeton Univ. Press, Princeton (1941; JFM 67.0384.01)], the tool is \textit{F. H. Szafraniec} [Ann. Polon. Math. 38, 43--47 (1979; Zbl 0412.46046)].