Richard F. Bass

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We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the “sampling problem for trigonometric polynomials”) and estimate the probability distribution of the condition number for the associated Vandermonde-type and Toeplitz-like matrices.(More)
BY RICHARD F. BASS AND XIA CHEN University of Connecticut and University of Tennessee If βt is renormalized self-intersection local time for planar Brownian motion, we characterize when Eeγβ1 is finite or infinite in terms of the best constant of a Gagliardo–Nirenberg inequality. We prove large deviation estimates for β1 and −β1. We establish lim sup and(More)
dXt = dWt + dAt , where Wt is d-dimensional Brownian motion with d ≥ 2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure πi as ∫ t 0 f (Xs)ds does to the measure f (x)dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures πi are members of the(More)