Abstract. Let G be a locally compact abelian group and A" be a Banach space. Let Ll(G, X) be the Banach space of X-valued Bochner integrable functions on G. We prove that the space of bounded linear translation invariant operators of L'(G, X) can be identified with L(X, M(G, X)), the space of bounded linear operators from X into M(G, X) where M(G, X) is the space of Jf-valued regular, Borel measures of bounded variation on G. Furthermore, if A is a commutative semisimple Banach algebra with identity of norm 1 then L\G, A) is a Banach algebra and we prove that the space of multipliers of L\G, A) is isometrically isomorphic to M{G, A). It also follows that if dimension of A is greater than one then there exist translationinvariant operators of Ll(G, A) which are not multipliers of L1(G, A).

A novel approach based on fourth order statistics is presented for estimating the parameters of the complex exponential signal model in additive colored Gaussian noise whose autocorrelation function is not known. Monte Carlo simulations demonstrate that the proposed method performs better than an existing method which also utilizes fourth order statistics under the similar noise condition. To deal with the non-stationarity of the modeled signal, various concepts are introduced while extending the estimation technique based on linear prediction to the higher order statistics domain. It is illustrated that the accuracy of parameter estimation in this case improves due to better handling of signal non-stationarity. While forming the fourth order moment/ cumulant of a signal, the choice of the lag-parameters is crucial. It has been demonstrated that the symmetric fourth order moment/ cumulant as defined in this paper will have many desirable properties.

ABSTRACT. Let AI, be commutative semlslmple Banach algebras and A 1 02 A 2 be their projective tensor product. We prove that, if A 10

Let G be a locally compact group and A an arbitrary Banach space. L p ( G , A ) {L^p}(G,A) will denote the space of p-integrable A-valued functions on G. M ( G , A ) M(G,A) will denote the space of regular A-valued Borel measures of bounded variation on G. In this paper, we characterise the relatively compact subsets of L p ( G , A ) {L^p}(G,A) . Using this result, we prove that if μ ∈ M ( G , A ) \mu \, \in \, M(G,A) , such that either x → μ x x\, \to \, {\mu _x} or x → x μ x{ \to _x}\mu is continuous, then μ ∈ L 1 ( G , A ) \mu \, \in \, {L^1}(G,A) .