Radha R

In this paper, it is shown that the class of right Fourier multipliers for the Sobolev space Wk,p(Hn) coincides with the class of right Fourier multipliers for Lp(Hn) for k ∈ ℕ, 1 < p < ∞. Towards this end, it is shown that the operators RjR̄jℒ-1 and RjR̄jRjℒ-1 are bounded on Lp(Hn), 1 < p < ∞, ℒ is the sublaplacian on Hn. This proof is based on the Calderon-Zygmund theory on the Heisenberg group. It is also shown that when p = 1, the class of right multipliers for the Sobolev space Wk,1(Hn) coincides with the dual space of the projective tensor product of two function spaces. © 2010 Akadémiai Kiadó, Budapest, Hungary.

It is well known that if m is an Lp-multiplier for the Fourier transform on ℝn, (1 < p < ∞) then there exists a pseudomeasure σ such that Tm f = σ * f. A similar problem is discussed for the Lp-Fourier multipliers for H-valued functions on the Heisenberg group, where H is a separable Hilbert space. © Springer-Verlag 2009.

Let G be a second countable locally compact abelian group. The aim of this paper is to characterize the left translates on the Heisenberg group [Formula presented] to be frames and Riesz bases in terms of the group Fourier transform.

The aim of this short paper is to prove a qualitative uncertainty principle namely Hardy’s theorem for the continuous wavelet transform.

A characterization is obtained for the Fourier transform of functions belonging to L2(R, H), where H denotes a Hilbert C∗-module. But in the case of functions belonging to L1(R, H) a similar result is proved when H is a separable Hilbert space.

The aim of this paper is to study sampling and reconstruction in a shift invariant space with multiple generators. On contrary to the classical case of a shift invariant space with a single generator, it is shown that Z cannot be a stable set of sampling for V(Φ) where Φ=Φ{ 1 , 2 ,..., n } when r ≥ 2. Further the problems of perturbation of a stable set of sampling and local reconstruction method are discussed along with an illustration and implementation.

For a class of continuously differentiable function ϕ satisfying certain decay conditions, it is shown that if the maximum gap δ:=supi⁡(xi+1−xi) between the consecutive sample points is smaller than a certain number B0, then any f∈V(ϕ) can be reconstructed uniquely and stably. As a consequence of this result, it is shown that if δ<1, then {xi:i∈Z} is a stable set of sampling for V(ϕ) with respect to the weight {wi:i∈Z}, where wi=(xi+1−xi−1)/2 and ϕ is the scaling function associated with Meyer wavelet. Further, the maximum gap condition δ<1 is sharp.

It is shown that a local reconstruction method from a nonuniform sampled data along with discrete wavelet transform and a simple statistical method is applicable in a voice system. © 2009 Elsevier Ltd. All rights reserved.

The paper deals with the necessary and sufficient conditions for obtaining reconstruction formulae and sampling theorems for every function belonging to the principal shift invariant subspace of L2(Hn), both in the time domain and a transform domain, where Hn denotes the Heisenberg group.

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on Rn and Cn under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved. © 2009 Elsevier Inc.