We introduce a certain subclass of multivalent analytic functions by making use of the principle of subordination between these functions and Cătas operator. Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties, and sufficient conditions for multivalent starlikeness are provide. The results pres...

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution in-tegrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this descript...

For a given p-valent analytic function g with positive coefficients in the open unit disk ∆, we study a class of functions f(z) = z + ∑∞ n=m anz , an ≥ 0 satisfying 1 p < ( z(f ∗ g)′(z) (f ∗ g)(z) ) < α ( z ∈ ∆; 1 < α < m+ p 2p ) . Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special ...

Given a set of n points in `1, how many dimensions are needed to represent all pairwise distances within a specific distortion? This dimension-distortion tradeoff question is well understood for the `2 norm, where O((logn)/ ) dimensions suffice to achieve 1 + distortion. In sharp contrast, there is a significant gap between upper and lower bounds for dimension reduction in `1. A recent result s...

We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers. We show that the mean-squared distortion of a vector quantizer designed from n independent and identically distributed (i.i.d.) data points using any design algorithm is at least (n ) away from the optimal distortion for some distribution on a bounded subset of R. Together ...

We derive new explicit bounds for the total variation distance between two convolution products of n ∈ N probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order are considered as well. We are interested in bounds with magic factors, i.e. roughly speaking n also appears in the denominator. Special emphasis is given...

Although Shannon introduced the concept of a rate distortion function in 1948, only in the last decade has the methodology for developing rate distortion function lower bounds for real-world sources been established. However, these recent results have not been fully exploited due to some confusion about how these new rate distortion bounds, once they are obtained, should be interpreted and shou...

Space-varying convolution often arises in the modeling or restoration of images captured by optical imaging systems. For example, in applications such as microscopy or photography the distortions introduced by lenses typically vary across the field of view, so accurate restoration also requires the use of space-varying convolution. While space-invariant convolution can be efficiently implemente...