Chow, Yun-shyong; Grenander, Ulf A singular perturbation problem. (English) Zbl 0587.45002 J. Integral Equations 9, No. 1, 63-73 (1985). For a fixed \(f\geq 0\), unimodal and integrable with compact support in [- 1,1], the authors consider the following modified convolution operator \(L_{\epsilon}\), defined by \[ (L_{\epsilon}g)(x)=(2\epsilon)^{- 1}\int^{x+\epsilon}_{x-\epsilon}f(y)g(y)dy\quad (\epsilon >0). \] This operator maps \(L^ 2(-1,1)\) into itself. Under some additional assumptions of f, it is shown that the eigenfunction \(\phi_{\epsilon}\) which corresponds to the largest eigenvalue of \(L_{\epsilon}\) converges weakly as \(\epsilon \to 0^+\) to a normal distribution. Reviewer: J.Burbea Cited in 1 ReviewCited in 1 Document MSC: 45C05 Eigenvalue problems for integral equations 45P05 Integral operators Keywords:singular perturbation problem; metric pattern theory; singular perturbation; convolution operator; eigenfunction; largest eigenvalue PDFBibTeX XMLCite \textit{Y.-s. Chow} and \textit{U. Grenander}, J. Integral Equations 9, No. 1, 63--73 (1985; Zbl 0587.45002)