in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

Arbitrary operator A on a Banach space X which is the generator of C0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse theorems on connection between the degree of smoothness of vector x ∈ X with respect to operator A, the rate of convergence to zero of the best approximation ...

The purpose of this paper is threefold: first to mainly review several recent results concerning the fine spectrum of the operator ∆v over the sequence spaces c and lp, where 1 < p < ∞; second to provide some new results concerning the residual spectrum and the continuous spectrum of the operator ∆v over the sequence spaces c and lp; and third to modify the definition of the operator ∆v and to ...

A Banach space X has the approximation property if and only if every compact set in X is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for Lp spaces and quotients of Lp spaces in terms of covering compact sets in X by operator ranges from Lp spaces. A Banach space X is a L1 space if and only if every compact set in X is ...

There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces Lp(μ), we get their coarse embeddability into a Hilbert space for 0 < p < 2. This together with a theorem by Banach and Mazur yields that coarse embeddability into l2 and into L...

Weighted Norm theory forms a basic component of the study of singular integrals. Here one attempts to characterize those measure spaces over which a broad class of singular integral operators remain bounded. For the case of singular integral operators on C-valued functions in Euclidean space, the answer is given by the Hunt-Muckenhoupt-Wheeden theorem [10]. It states that the necessary and suff...

In this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted Dirichlet spaces or Bloch type spaces to $Q_K$ type spaces.

This paper introduces a generalized formulation of linear prediction (LP), including both conventional and temporally weighted LP analysis methods as special cases. The temporally weighted methods have recently been successfully applied to noise robust spectrum analysis in speech and speaker recognition applications. In comparison to those earlier methods, the new generalized approach allows mo...

Following earlier work, we modify linear predictive (LP) speech analysis by including temporal weighting of the squared prediction error in the model optimization. In order to focus this so called weighted LP model on the least noisy signal regions in the presence of stationary additive noise, we use shorttime signal energy as the weighting function. We compare the noisy spectrum analysis perfo...