In terms of Wright generalized hypergeometric function we define a class of analytic functions. The class generalize well known classes of k-starlike functions and k-uniformly convex functions. Necessary and sufficient coefficient bounds are given for functions in this class. Further distortion bounds, extreme points and results on partial sums are investigated.

In this paper we calculate the asymptotics of various moments of the central values of Rankin-Selberg convolution L-functions of large level, thus generalizing the results and methods of W. Duke, J. Friedlander, and H. Iwaniec and of the authors. Consequences include convexity-breaking bounds, nonvanishing of a positive proportion of central values, and linear independence results for certain H...

Sparse blind deconvolution is the problem of estimating the blur kernel and sparse excitation, both of which are unknown. Considering a linear convolution model, as opposed to the standard circular convolution model, we derive a sufficient condition for stable deconvolution. The columns of the linear convolution matrix form a Riesz basis with the tightness of the Riesz bounds determined by the ...

In the present work, authors introduce a new linear differential operator associated with $ q $-calculus which uses $-derivative operator. For class involving operator, interesting properties like coefficient inequality, growth, distortion, convolution and radii of starlikeness are established. Various connections that earlier works pointed out.

A comprehensive class of complex-valued harmonic prestarlike univalent functions is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Distortion bounds and extreme points are also obtained. 2000 Mathematics Subject Classification:Primary 30C45, 30C50.

We prove that convolution with arclength measure on the curve parametrized by h(t) := (t, t, . . . , t) is a bounded operator from L(R) to L(R) for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.

In [15], Hoffstein and Hulse defined the shifted convolution series of two cusp forms by “shifting” the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of certain values of these series and prove a polynomial bound as h → ∞. Our method relies on a result of Mertens and Ono [22], who showed that these values ...

We describe an outdoor mobile robot navigation and localisation system based on a new visual feature detector designed for wide-angle image sequences. Wide-angle images exhibit significant radial distortion for which existing scale-space detectors such as SIFT are inappropriate. We argue that the required scale-space images can be correctly obtained through the convolution of the image, mapped ...

We revisit the complexity of online computation in the cell probe model. We consider a class of problems where we are first given a fixed pattern or vector F of n symbols and then one symbol arrives at a time in a stream. After each symbol has arrived we must output some function of F and the n-length suffix of the arriving stream. Cell probe bounds of Ω(δ lg n/w) have previously been shown for...