An Analytic Version of Wiener-Itô Decomposition on Abstract Wiener Spaces

An Infinitesimal Approach to Stochastic Analysis on Abstract Wiener Spaces

The Wiener Transform on the Besicovitch Spaces

In his fundamental research on generalized harmonic analysis, Wiener proved that the integrated Fourier transform defined by Wf(γ) = ∫ f(t) (e−2πiγt − χ[−1,1](t))/(−2πit) dt is an isometry from a nonlinear space of functions of bounded average quadratic power into a nonlinear space of functions of bounded quadratic variation. We consider this Wiener transform on the larger, linear, Besicovitch ...

Stepanov’s Theorem in Wiener spaces

One generalization of this result has been given in [BRZ], when the domain X is a metric measure space. In this case, the authors deal with metric spaces endowed with a doubling measure and supporting Poincaré-type inequalities. Both conditions ensure the existence of a strong measurable differentiable structure on the space X which provides a differentiation theory for Lipschitz functions in t...

Computing Wiener and hyper–Wiener indices of unitary Cayley graphs

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

On a certain semiclassical problem on Wiener spaces

We study asymptotic behavior of the spectrum of a Schrödinger type operator LV = L− λV on the Wiener space as λ→∞. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.