Approximation in reflexive Banach spaces and applications to the invariant subspace problem

We formulate a general approximation problem involving reflexive and smooth Banach spaces, and give its explicit solution. Two applications are presented— the first is to the Bounded Completion Problem involving approximation of Hardy class functions, while the second involves the construction of minimal vec- tors and hyperinvariant subspaces of linear operators, generalizing the Hilbert space technique of Ansari and Enflo

Digital phase-locked loops tracked by a relay sensor

An optimal algorithm is presented for tracking the phase of a slowly modulating signal by means of digital sampling of its sign. Error bounds and a numerical illustration are given

Approximation in reflexive Banach spaces and applications to the invariant subspace problem

We formulate a general approximation problem involving reflexive and smooth Banach spaces, and give its explicit solution. Two applications are presented— the first is to the Bounded Completion Problem involving approximation of Hardy class functions, while the second involves the construction of minimal vec- tors and hyperinvariant subspaces of linear operators, generalizing the Hilbert space technique of Ansari and Enflo

Paired kernels and their applications

This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Results on near-invariance properties, representations, and inclusion relations for these kernels are obtained. The existence of a minimal Toeplitz kernel containing any projected paired kernel and, more generally, any nearly $S^*$-invariant subspace of $H^2$, is derived. The results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.Comment: 26 page

Readiness to change drinking behaviour among heavy-drinking university students in England

There is growing literature on possible ways of reducing alcohol consumption and alcohol-related harm among university students (Larimer and Cronce, 2002; Siegers and Carey, 2010). However, interventions with this aim might be made more effective by information on students’ readiness to change their drinking behaviour (Carey et al., 2007a), where an assessment of readiness to change might influence the kind of approach that is thought most likely to be successful. For example, it has been found that readiness to change moderated the effects of a brief intervention among heavy-drinking students (either brief motivational intervention or alcohol expectancy challenge) such that high readiness to change made an expectancy challenge relatively more effective in reducing drinking (Capone and Wood, 2009). This study also reported an association between higher readiness to change and greater reductions in alcohol consumption in the overall sample, thus supporting previous findings (Fromme and Corbin, 2004; Carey et al., 2007b). Although high readiness to change may increase the chances of successful brief intervention among heavy-drinking students, it has been found that, even among individuals referred to a university-based alcohol intervention programme, there was limited acknowledgement of a drinking problem or interest in changing behaviour (Caldwell, 2002; Vik et al., 2000). Such research has been conducted mainly in the USA and, with the exception of one study (Hosier, 2001), it is unknown whether a comparable lack of concern about heavy drinking is true of students in England. Moreover, there is limited understanding of the different factors associated with, and predictive of, readiness to change in heavy-drinking students. The aims of this paper are therefore (i) to assess levels of readiness to change among heavy-drinking students at universities in England, (ii) to identify variables predictive of readiness to change among heavy-drinking students and (iii) to generate hypotheses that could be tested in further research

Kernels of unbounded Toeplitz operators and factorization of symbols

We consider kernels of unbounded Toeplitz operators in Hp(C+) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in Hp(C+), we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involving two different Hardy spaces and we establish relations between the kernels of two operators whose symbols differ by a factor which corresponds, in the unit circle, to a non-integer power of z. We apply the results to describe the kernels of Toeplitz operators with non-vanishing piecewise continuous symbols.This work was partially supported by FCT/Portugal through UID/MAT/04459/2020. The research of M. T. Malheiro was partially supported by Portuguese Funds through FCT/Portugal within the Projects UIDB/00013/2020 and UIDP/00013/2020

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an Hp setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are establishedFCT/Portuga

Is Contamination Good or Bad? A Corpus-assisted Case Study in Translating Evaluative Prosody

In this article we showcase the relevance of corpus evidence in examining potential differences in evaluative prosody in the use of two seeming translation equivalents, namely the Italian noun contaminazione and its French "lookalike" contamination. Our analysis suggests that, when the item is used literally, its evaluative prosody is negative in both languages. However, when used figuratively (particularly in cultural and artistic contexts) the prosody of the Italian contaminazione is neutral or positive, whereas this figurative, positive use does not appear to be shared by French contamination. On the basis of these observations, we reflect on the role of corpus analysis in raising awareness of evaluative prosody, in particular how the \u201csame\u201d item can have a different evaluative prosody when used literally or figuratively, and how lookalike items can have a different evaluative prosody across languages \u2013 an especially tricky issue for language learners and professionals. In the final part of our work, we make proposals for a further, more exploratory use of corpus methods (relying in particular on collocates) for identifying cross-linguistic correspondences