Gohberg lemma, compactness, and essential spectrum of operators on compact Lie groups

In this paper we prove a version of the Gohberg lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators on compact Lie groups. As a consequence, we prove several results on bounds for the essential spectrum and a criterion for an operator to be compact. The conditions are given in terms of the matrix-valued symbols of operators.Comment: 13 page

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on $X$. This extends the result for analytic functions on compact manifold by Seeley, and the characterisation of Gevrey functions and Gevrey ultradistributions on compact Lie groups and homogeneous spaces by the authors.Comment: 19 pages; updated and corrected final version, to appear in Trans. Amer. Math. So

Hilbert-Schmidt and Trace Class Pseudo-differential Operators on the Abstract Heisenberg Group

In this paper we introduce and study pseudo-differential operators with operator valued symbols on the abstract Heisenberg group $\mathbb{H}(G):=G \times \widehat{G} \times \mathbb{T},$ where $G$ a locally compact abelian group with its dual group $\widehat{G}$. We obtain a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert-Schmidt operators. As a key step in proving this we derive a trace formula for the trace class $j$-Weyl transform, $j \in \mathbb{Z}^*$ with symbols in $L^{2}(G\times \widehat{G}).$ We go on to present a characterization of the trace class pseudo-differential operators on $\mathbb{H}(G)$. Finally, we also give a trace formula for these trace class operators.Comment: 16 page

Pseudo-Differential Operators, Wigner Transform, and Weyl Transform on the Affine Poincar\'e Group

In this paper, we study harmonic analysis on the affine Poincar\'e group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness properties of pseudo-differential operators on $\mathcal{P}_{aff}$. We also provide a necessary and sufficient condition on the operator-valued symbols such that the corresponding pseudo-differential operators are in the class of Hilbert--Schmidt operators. Consequently, we obtain a characterization of the trace class pseudo-differential operators on the Poincar\'e affine group $\mathcal{P}_{aff}$, and provide a trace formula for these trace class operators. Finally, we study the Wigner transform, and Weyl transform associated with the operator valued symbol on the Poincar\'e affine group $\mathcal{P}_{aff}$

Systematic Measurement Error in Self-Reported Health: Is anchoring vignettes the way out?

This paper studies the pattern of non-random measurement error in self-assessed health responses across population subgroups and examines whether anchoring of vignettes can be used to identify this bias. It uses unique data from the World Health Survey (WHS)-SAGE survey(wave 1) from India, that has self-reported assessments of health linked to anchoring vignettes as well as objective measures like measured anthropometrics and performance tests on a range of health domains. Both estimations using individual fixed effects and anchored-vignettes response reveal strong systematic reporting bias across subgroups. Controlling for a battery of objective health measures, we implicitly test and confirm the validity of the ‘response consistency’ assumption used in vignettes technique. Further analysis using individual fixed effects in a two-stage regression estimation reveals substantial individual reporting bias even after accounting for the usual covariates controlled in a regression. The analysis finds that non-random measurement error in SAH cannot be simply dealt with by controlling for socio-economic covariates in a typical regression framework. This exposes the problem of cross-comparability using self-reported health response in the context of a developing country setting and lends support to the use of vignettes for identifying this bias

Does Women Empowerment Predict Contraceptive Use? A Study in a Rural Area of Hooghly District, West Bengal

Background: India launched the world’s first national family planning programme in 1952. Unfortunately, considerable numbers of eligible couples in India are still not using any method of contraception in spite of the fact that knowledge related to contraceptives are not lacking. Studies reported that the status of the women in the family and largely in the community, represented by a measure ‘women empowerment’ plays a role in determining contraceptive use. However, there is dearth of literature in this regards especially among women of reproductive age of West Bengal. Aims & Objectives: To find out the current contraceptive use and its relationship, if any with women empowerment among adult married women of reproductive age group in a rural area of West Bengal. Material & Methods: Community based cross-sectional study was conducted among 151 WRA using interviewer-administered questionnaire. Current use of contraceptive was the outcome variable. The main explanatory variable was ‘empowerment score’-a summed measure of four domains: ‘financial autonomy’, ‘freedom of movement’, ‘involvement in household level decision making’ and ‘woman’s power in sexual and reproductive decision making’. Results: 63.6% study participants were using any method of contraception at the time of study. Women empowerment [AOR (CI): 1.11 (1.02-1.22)] and education of women [AOR (CI): 2.56 (1.13-5.85)] were significantly associated with contraceptive use, even after adjustment with other independent variables. Conclusion: Educating women and empowering them will improve the family planning practices. This will, in long run play a pivotal role in improving family and community health

Domestic unintentional injury of 1 to 5-year-old children in a rural area of West Bengal, India: a community-based study

Background: Childhood unintentional injury, a major public health problem in India, is largely preventable. The aim of this study was to determine the burden and determinants of unintentional injury of 12 to 59 months old child at household level.Method: A community based cross-sectional study was conducted at Singur block, Hooghly district, West Bengal, India among randomly chosen children using a predesigned and pretested interviewer administered questionnaire and a checklist for assessing household level injury hazard during the period of November 2015 to February 2016. Parental supervisory behaviour was assessed using PSAPQ questionnaire. Multivariable logistic regression was performed using SPSS 19.0 software.Result: A total of 163 were involved in the study. Over one-third (37.4%) of the children underwent any type of injury during last 3-month time period, predominant body part being upper limb. Parental supervisory behaviour [AOR-2.6, (95% CI-1.2-4.9)] and household level injury hazard (AOR-1.55, 95% CI- 1.3-1.7)] were found to be significant predictors of unintentional injury.Conclusion: Unintentional injury among children is prevalent in West Bengal in India. Dissemination of injury prevention information with special focus on household modification and increased parental supervision are effective strategies to prevent unintentional injury