We provide leading-order asymptotics for the size of the gap in the zeros
around 1 of paraorthogonal polynomials on the unit circle whose Verblunsky coefficients
satisfy a slow decay condition and are inside the interval (?1, 0). We also
include related results that impose less restrictive conditions on the Verblunsky coefficients.

We study the problem of when the collection of the recession cones of a
polyhedral complex also forms a complex.We exhibit an example showing that this is
no always the case. We also show that if the support of the given polyhedral complex
satisfies a Minkowski–Weyl-type condition, then the answer is positive.

We provide an existence and uniqueness theory for an extension of
backward SDEs to the second order.While standardBackward SDEs are naturally connected
to semilinear PDEs, our second order extension is connected to fully nonlinear
PDEs, as suggested in Cheridito et al. (Commun. Pure Appl.Math. 60(7):1081–1110,
2007). In particular, we provide a fully nonlinear extension of the Feynman–Kac.

A number of image denoising models based on higher order
parabolic partial differential equations (PDEs) have been proposed in an
effort to overcome some of the problems attendant to second order methods
such as the famous Perona–Malik model. However, there is little
analysis of these equations to be found in the literature.

We introduce first weighted function spaces on Rd using the
Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations
of these spaces by decomposition of functions. Next we
obtain in the real line and in radial case on Rd weighted Lp-estimates
of the Dunkl transform of a function in terms.