Parseval frames can be thought of as redundant or linearly dependent coordinate systems for Hilbert spaces, and have important applications in such areas as signal processing, data compression, and sampling theory. We extend the notion of a Parseval frame for a fixed Hilbert space to that of a moving Parseval frame for a vector bundle over a manifold. Many vector bundles do not have a moving ba...

We provide unipotent factorizations of vector bundle automorphisms real and complex bundles over finite dimensional locally CW-complexes. This generalizes work Thurston–Vaserstein Vaserstein for trivial bundles. also address two symplectic cases propose a geometric analog the problem in setting holomorphic Stein manifolds.

We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain a subcategory of k-fold vector bundles consisting of symmetric k-fold vector bundles equipped with a family of morphisms indexed by the symmetric g...

In this paper, we generalize the notion of vector fields on Weil bundle. Let $q\geq 2$ be an integer, give equivalent definitions a $q$-vector field bundle in terms $q$-derivations. Further, construct Lie graded algebra structure multivector