A theorem on trigonometric integrals

Some Divergent Trigonometric Integrals

1. Introduction. Browsing through an integral table on a dull Sunday afternoon some time ago, I came across four divergent trigonometric inte-grals. (See (1) and (2) below.) I was intrigued as to how these divergent integrals ended up in a respectable table. Tracing their history, it turned out they were originally " evaluated " when some convergent integrals, (5) and (6), were differentiated u...

Integrals and Summable Trigonometric Series

is that of suitably defining a trigonometric integral with the property that, if the series (1.1) converges everywhere to a function ƒ(x), then f(x) is necessarily integrable and the coefficients, an and bn, given in the usual Fourier form. It is well known that a series may converge everywhere to a function which is not Lebesgue summable nor even Denjoy integrable (completely totalisable, [3])...

On the Exponent of Convergence of Trigonometric Integrals

On iterative evaluation of extrema of integrals of trigonometric polynomials

A Class of Double Integrals Involving Gaussian and Trigonometric Factors