Jacob's ladders and the ${\tilde{Z}}^2$-transformation of the orthogonal system of trigonometric functions

Abstract

It is shown in this paper that there is a continuum set of orthogonal systems relative to the weight function ${\tilde{Z}}^2(t)$. The corresponding integrals cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.

References in corpus (2)

• Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral
• Jacob's ladders and the quantization of the Hardy-Littlewood integral