A Type of Orthonormal Bases on 2-*-Inner Product Spaces

In this paper, we define an orthonormal basis for 2-*-inner product space and obtain some useful results. Moreover, we introduce a 2-norm on a dense subset of a 2-*-inner product space. Finally, we obtain a version of the Selberg, Buzano’s and Bessel inequality and its results in an A-2-inner product space.

SQUARE OF THE ERROR OCTONIONIC THEOREM AND HYPERCOMPLEX FOURIER SERIES

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions. </span></p></div></div></div>

HARMONIC ANALYSIS OF THE LEBEDEV-STIELTJES INTEGRALS

We expand the Bochner technique on the following Lebedev-Stieltjes integrals [Formula: see text] which are related to the Kontorovich-Lebedev transformation. Mapping and inversion properties are investigated. The Fourier type series with respect to an uncountable orthonormal system of the modified Bessel functions are considered in the Bohr type pre-Hilbert space. The Bessel inequality and Parseval equality are proved.

On the Boas-Bellman inequality in inner product spaces

New results related to the Boas–Bellman generalisation of Bessel' inequality in inner product spaces are given.