Orthogonality on sets

Strong forms of orthogonality for sets of hypercubes

Strong forms of orthogonality for sets of frequency hypercubes

For frequency hypercubes of dimension d > 2, we discuss several generalizations of the usual notion of pairwise orthogonality. We provide some constructions for complete sets of orthogonal frequency hypercubes. 1. Strong orthogonality for frequency hypercubes In this paper we will examine strong forms of orthogonality for frequency hypercubes. The standard de nition requires that each ordered p...

On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

On Orthogonality of Latin Squares

Abstract: A Latin square arrangement is an arrangement of s symbols in s rows and s columns, such that every symbol occurs once in each row and each column. When two Latin squares of same order superimposed on one another, then in the resultant array every ordered pair of symbols occurs exactly once, then the two Latin squares are said to be orthogonal. A frequency square M of type F (n; λ) is ...

Global Orthogonality Implies Local Almost-orthogonality

We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums. 0. Introduction. First, an apology. The title, though correct, is somewhat misleading. It should be “Global almostorthogonality implies...