Ditkin’s condition for certain Beurling algebras

We use methods of harmonic analysis and group representation theory to estimate memory decay of the inverse operators in Banach spaces. The memory of the operators is defined using the notion of the Beurling spectrum. We obtain a general continuous non-commutative version of the celebrated Wiener's Tauberian lemma with estimates of the "Fourier coefficients" of inverse operators. In particular, we generalize various estimates of the elements of the inverse matrices. The results are illustrated with a variety of examples including integral and integrodifferential operators.

show abstract

Memory estimation of inverse operators

Баскаков

Krishtal

2014

Journal of Functional Analysis

View full text Add to dashboard Cite

show abstract

Completeness of eigenvectors of group representations of operators whose Arveson spectrum is scattered

Huang

1999

Proc. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

Abstract. We establish the following result.Theorem. Let α : G → L(X) be a σ(X, X * ) integrable bounded group representation whose Arveson spectrum Sp(α) is scattered. Then the subspace generated by all eigenvectors of the dual representation α * is w * dense in X * . Moreover, the σ(X, X * ) closed subalgebra Wα generated by the operators αt (t ∈ G) is semisimple.If, in addition, X does not contain any copy of c 0 , then the subspace spanned by all eigenvectors of α is σ(X, X * ) dense in X. Hence, the representation α is almost periodic whenever it is strongly continuous. Spectral theory for integrable bounded group representationsThroughout this paper G will denote a locally compact abelian (LCA) group with identity e and G will denote the dual group of G. The multiplication on LCA groups will be written by addition. Let L 1 (G) (resp. M(G)) be the usual group algebra (resp. measure algebra) with convolution as product operation. We refer to [11] or [21] for basic knowledge of Harmonic Analysis on LCA groups.Given a complex Banach space X, let L(X) be the Banach algebra of all bounded linear operators on X. Take a LCA group G. A bounded group representation α of G on X is a mapping α : G → L(X) satisfying the following properties:(a) Group property: α e = I X the identity operator on X and α s+t = α s α t for all s, t ∈ G; (b) Boundedness: α := sup t∈G α t < ∞. Moreover, α is called strongly (resp. weakly) continuous if for each x ∈ X the mapping t → α t x is norm (resp. weakly) continuous. We need a further notion. Definition 1.1. A bounded group representation α : G → L(X) of G on X is called integrable if there exists a subspace X * ⊂ X * satisfying the following

show abstract

A Novel Method for Speech Acquisition and Enhancement by 94 GHz Millimeter-Wave Sensor

Chen

Sheng

et al. 2015

Sensors

View full text Add to dashboard Cite

In order to improve the speech acquisition ability of a non-contact method, a 94 GHz millimeter wave (MMW) radar sensor was employed to detect speech signals. This novel non-contact speech acquisition method was shown to have high directional sensitivity, and to be immune to strong acoustical disturbance. However, MMW radar speech is often degraded by combined sources of noise, which mainly include harmonic, electrical circuit and channel noise. In this paper, an algorithm combining empirical mode decomposition (EMD) and mutual information entropy (MIE) was proposed for enhancing the perceptibility and intelligibility of radar speech. Firstly, the radar speech signal was adaptively decomposed into oscillatory components called intrinsic mode functions (IMFs) by EMD. Secondly, MIE was used to determine the number of reconstructive components, and then an adaptive threshold was employed to remove the noise from the radar speech. The experimental results show that human speech can be effectively acquired by a 94 GHz MMW radar sensor when the detection distance is 20 m. Moreover, the noise of the radar speech is greatly suppressed and the speech sounds become more pleasant to human listeners after being enhanced by the proposed algorithm, suggesting that this novel speech acquisition and enhancement method will provide a promising alternative for various applications associated with speech detection.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Ditkin’s condition for certain Beurling algebras

Cited by 3 publications

References 14 publications

Memory estimation of inverse operators

Memory estimation of inverse operators

Completeness of eigenvectors of group representations of operators whose Arveson spectrum is scattered

A Novel Method for Speech Acquisition and Enhancement by 94 GHz Millimeter-Wave Sensor

Contact Info

Product

Resources

About