We define real-valued characteristic classes of flat complex vector bundles and flat real vector bundles with a duality structure. We construct pushforwards of such vector bundles with vanishing characteristic classes. These pushforwards involve the analytic torsion form in the first case and the eta-form of the signature operator in the second case. We show that the pushforwards are independen...

The vector x is called supercyclic for T ifC orb T, x is dense inH. Also a supercyclic operator is one that has a supercyclic vector. For some sources on these topics, see 1–16 . Let H be a separable Hilbert space of functions analytic on a plane domain G such that, for each λ in G, the linear functional of evaluation at λ given by f → f λ is a bounded linear functional on H. By the Riesz repre...

In this paper we develope the fundamentals of the generalized symplectic geometry on the bundle of linear frames LM of an n-dimensional manifold M that follows upon taking the R-valued soldering 1-form θ on LM as a generalized symplectic potential. The development is centered around generalizations of the basic structure equation df = −Xf ω of standard symplectic geometry to LM when the symplec...

Functions on the double coset space K\G/K, where G is a group and K is a subgroup of G are called spherical functions. One can also study functions on G/K with values in a representation V of G which are equivariant with respect to the left action of K. This more general class of functions may be called vector valued spherical functions. The theory of such functions was developed by Harish-Chan...

In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolm...

The purpose of this paper is to elucidate a dichotomy between past and future in prediction of multivariate time-series. More specifically, vector-valued gaussian stochastic processes may be deterministic in one time-direction and not the other. This fact, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shift-operator. The exposition and the examples we discu...

We show that any decoherence functional D can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural map U from the history Hilbert space K to the standard Hilbert space H of the usual quantum formulation. We show that U is an isomorphism from K onto a closed s...