We consider the time–continuous doubly–dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this is result is a new Szegö formula for certain pseudo–differential operators. The formula j...

We consider the time–continuous doubly–dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this result is a new Szegö formula for certain pseudo–differential operators. The formula just...

This note proves sharp affine Gagliardo-Nirenberg inequalities which are stronger than all known sharp Euclidean Gagliardo-Nirenberg inequalities and imply the affine L−Sobolev inequalities. The logarithmic version of affine L−Sobolev inequalities is verified. Moreover, An alternative proof of the affine Moser-Trudinger and Morrey-Sobolev inequalities is given. The main tools are the equimeasur...

In the present paper, sharp upper bounds of |a3 − μa2| for the functions f(z) = z+ a2z + a3z + ... belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractiona...

For non-zero complex b, let N b m,n(φ) (m > n), m ∈ N, n ∈ N0 denote the class of normalized univalent functions f satisfying 1+ 1 b ( Df(z) Dnf(z) − 1 ) ≺ φ(z), z in the open unit disk U , where Dnf denotes the Sălăgean derivative of f . In this paper, we obtain sharp bounds for the Fekete-Szegö functional |a3 − μa2|.