Let fW(t); 0 t 1g be a real-valued Wiener process, starting from 0. For a large class of functions f which may vanish at 0, we obtain the exact asymptotics, as " goes to 0, of log P(sup 0<t1 jW(t)=f(t)j < ").

We show that for a Jacobi operator with coefficients whose (j + 1)’th moments are summable the j’th derivative of the scattering matrix is in the Wiener algebra of functions with summable Fourier coefficients. We use this result to improve the known dispersive estimates with integrable time decay for the time dependent Jacobi equation in the resonant case.

We consider the problem of semi-cardinal interpolation for polyharmonic splines. For absolutely summable data sequences, we construct a solution to this problem using a Lagrange series representation. The corresponding Lagrange functions are deened using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.

We show that for a one-dimensional Schrödinger operator with a potential, whose (j + 1)-th moment is integrable, the j-th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schrödinger equation in the resonant case.

We define a Fourier transform and a convolution product for functions and distributions on Heisenberg–Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley–Wiener–Schwartz theorem, and define a convolution Banach algebra.

The Wiener polarity indexWP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation between Wiener polarity index and Zegreb indices, and the relation between Wiener polarity index and Wiener index (resp. hyper-Wiener index). Moreover, we determine the second smallest Wiener polarity index t...

This paper describes two novel Wiener-based approaches for frame-to-frame image registration. The first approach, Local Wiener Registration, incorporates the crosscorrelation between the two frames to determine the Wiener filter at each pixel location in order to predict the second frame from the first frame. The second approach, Block Wiener Registration, divides the image in nonoverlapping bl...