In this paper, we investigate the relation between L-projections and conditional expectations on subalgebras of the Fourier Stieltjes algebra B(G), and we will show that compactness of G plays an important role in this relation.

As an alternative to cumbersome nonlinear schemes for dimensionality reduction, the technique of random linear projection has recently emerged as a viable alternative for storage and rudimentary processing of high-dimensional data. We invoke new theory to motivate the following claim: the random projection method may be used in conjunction with standard algorithms for a multitude of machine lea...

A power-law correlation based on an inverse filter Fourier-Radon-transform synthetic discriminant function (SDF) for facial recognition is proposed. In order to avoid spectral overlap and nonlinear crosstalk, superposition of rotationally variant sets of inverse filter Fourier-transformed Radon-processed templates is used to generate the SDF. For the inverse filter, the Fourier transform of M p...

We give suucient conditions to approximate the \nonessential" spectrum of a bounded operator L acting on a Banach space B by part of the spectra of a sequence of compact (or nite rank) operators L j = (Id ? j)L(Id ? j), where Id ? j is a suitable family of uniformly bounded operators which approach the identity. (By nonessential spectrum we mean here all the spectrum outside of the disc of radi...

We study symplectic manifolds (M, ω) equipped with a symplectic torsion-free affine (also called Fedosov) connection ∇ and admitting a metaplectic structure. Let S be the so called symplectic spinor bundle and let R be the curvature tensor field of the symplectic spinor covariant derivative ∇ associated to the Fedosov connection ∇. It is known that the space of symplectic spinor valued exterior...

We examine, from a geometrical point of view, the dynamics of a relativistic extended object with loaded edges. In the case of a Dirac-Nambu-Goto [DNG] object with DNG edges, the worldsheet m generated by the parent object is, as in the case without boundary, an extremal timelike surface in spacetime. Using simple variational arguments, we demonstrate that the worldsheet of each edge is a const...

We prove the following results for a unital simple direct limit A of recursive subhomogeneous algebras with no dimension growth: (1) tsr(A) = 1. (2) The projections in M∞(A) satisfy cancellation: if e ⊕ q ∼ f ⊕ q, then e ∼ f . (3) A satisfies Blackadar’s Second Fundamental Comparability Question: if p, q ∈ M∞(A) are projections such that τ(p) < τ(q) for all normalized traces τ on A, then p q. (...

We give conditions on a general family $P_{\lambda}:\R^n\to\R^m, \lambda \in \Lambda,$ of orthogonal projections which guarantee that the Hausdorff dimension formula $\dim A\cap P_{\lambda}^{-1}\{u\}=s-m$ holds generically for measurable sets $A\subset\Rn$ with positive and finite $s$-dimensional measure, $s>m$, lower density. As an application we prove $A,B\subset\Rn$ $s$- $t$-dimensional meas...

Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. Relying basis projections commuting with A, we construct almost-unitary that diagonalizes modulo infinitely smoothing operator. We provide invariant algorithm for the computation its full symbol, as well explicit...