An extremal problem and inequalities for entire functions of exponential type
The task addressed in this article is bounding integrals of functions of exponential type \(f\) by their values at the origin; those values must not be zero and the integrands nonnegative. The integrals are over the whole real axis. This makes them a so-called one-delta-function. The infimum \(\mathcal{A}\) of these upper bounds are also required. In the classical case the solution is \(\mathcal{A}=1\) and the argmin function is the square of the sinc function.\N\NAn advanced problem of this type is when the integrands are explicitly required to be radially monotone, i.e., increasing/decreasing for the arguments going from \(-\infty\) to \(0\) and from the origin to \(+\infty\), respectively. This problem is solved with \(\mathcal{A}\in(1.2750,1.27714)\).
scientific article; zbMATH DE number 7875283
scientific article