In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere Sn ≃ SO(n + 1)/SO(n) and the spherical functions of the n-dimensional real projective space P n(R) ≃ SO(n + ...

We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the ...

We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three-dimensional projective space. This problem is first turned into the computation ...

In this note, we prove that for any two orthogonal projections PT,PS on a Hilbert the well-known norm formulas ‖PT+PS‖=1+‖PTPS‖, unless PT=PS=0 and ‖PTPS+PSPT‖=‖PTPS‖2+‖PTPS‖, can be derived from each other. Such result ...

In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R ...

Let H be a Hilbert space and L(H) be the algebra of all bounded linear operators from H to H. Our goal in this article is to study the set P⋅Lh of operators in L(H) that can be factorized as the product of an orthogonal ...