Under suitable conditions on a measure, universality limits f ( ; ) that arise in the bulk, unitary case, are reproducing kernels of de Branges spaces of entire functions. In the classical case, f is the sinc kernel f (s; t) = sin (s t) (s t) ; but other kernels can arise. We study the linear operator L [h] (x) = Z 1 1 f (s; x)h (s) ds; establishing inequalities, and deducing some conditions fo...

Tyrone Duncan has made seminal contributions in the field of Filtering, Stochastic Control and the interface of probability theory and geometry. In his pioneering thesis, he presented a fundamental theory of nonlinear filtering and was instrumental in introducing the modern theory of martingales as developed by Doob, Meyer, Kunita-Watanabe and others in the study of nonlinear filtering. As he s...

We prove regularity (i.e., smoothness) of measures on R d satisfying the equation L = 0 where L is an operator of type Lu = tr(Au 00) + B ru. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely-square integrable. We also treat a class of corresponding innnite dimensional cases where IR d is replaced by a locally convex topological vector space X. In this cases...

In this paper we prove two theorems relating positive definite measures to induced representations. The first shows how the injection of a positive definite measure on a topological group H into a containing locally compact group G in which H is closed gives rise to induced representations. The second is another version of Mackey's imprimitivity theorem, along the lines of Loomis' proof [5]. We...

The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...