We prove variants of Wiener's Tauberian theorem in the framework quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or two operators. Our results include as special case. Applications our theorems are related to localization operators, Toeplitz isomorphism Bargmann-Fock spaces quantization schemes with consequences Shubin's pse...

An α-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter α > 0 represents a mean reversion force to zero. We generalize the notion of α-Wiener bridges to continuous functions α : [0, T ) → R. We show that if the limit limt↑T α(t) exists and is positive, then a general α-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T wi...

Different versions of Wiener’s Tauberian theorem are discussed for the generalized group algebra LI(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener’s Tauberian property is introduced and it is proved that LI(G,A) is weakly Tauberian if and only if A is....

The present paper involves the approximation of nonlinear systems using Wiener/Volterra models with Kautz orthonormal functions. It focuses on the problem of selecting the free complex pole which characterizes these functions. The problem is solved by minimizing an upper bound of the error arising from the truncated approximation of Volterra kernels using Kautz functions. An analytical solution...

We prove a topological Paley-Wiener theorem for the Fourier transform deened on the real hyperbolic spaces SO o (p; q)=SO o (p ? 1; q), for p; q 2 2N, without restriction to K-types. We also obtain Paley-Wiener type theorems for L-Schwartz functions (0 < 2) for xed K-types.

Econometricians are liable to regard discrete-time autoregressive moving-average (ARMA) models as approximations to continuous-time stochastic differential equations. (For a recent exposition of this point of view, see Sims 2010.) In common with other statisticians, they tend to assume that the differential equations are powered by the increments of a Wiener process. A Wiener process is formed ...

We prove a Wiener-Tauberian theorem for the L1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz type theorem for complex groups. As a corollary we obtain a Wiener-Tauberian type result for compactly supported distributions.

We propose a set-indexed family of capacities {cap G } G⊆R + on the classical Wiener space C(R +). This family interpolates between the Wiener measure (cap {0}) on C(R +) and the standard capacity (cap R +) on Wiener space. We then apply our capacities to characterize all quasi-sure lower functions in C(R +). In order to do this we derive the following capacity estimate (Theorem 2.3) which may ...