Early work of N.G. (Dick) de Bruijn in analysis and some of my own

There are parallels between de Bruijn’s early work in analysis and that of the author. However, Dick’s work soon became much broader and deeper. While the present paper reviews several topics of common interest, its main content is a short version of Dick’s important article related to Riemann’s Hypothesis, entitled ‘The roots of trigonometric integrals’ [N.G. de Bruijn, The roots of trigonometric integrals, Duke Math. J. 17 (1950) 197–226]. The associated ‘de Bruijn–Newman constant’ is also discussed.