We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation in a time-dependent potential and we ...

The metric increasing property of the exponential map is known to be equivalent to the fact that the set of positive definite matrices is a Riemannian manifold of nonpositive curvature. We show that this property is an easy consequence of the logarithmic-geometric mean inequality for positive numbers. Operator versions of this inequality lead to a generalisation of the exponential metric increa...

let a(p) denote the class of functions which are analytic in the open unit disk u. by making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

We conjecture the following so-called norm compression inequality for 2×N partitioned block matrices and the Schatten p-norms: for p ≥ 2,

The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity. The message of the paper is to reveal some kind of a kink: the pth Schatten norm increases as n to the power 1/p before the singularity reaches a critical point and as n to an exponent depending on the singularity be...

In this paper, we fully characterize the duality mapping over space of matrices that are equipped with Schatten norms. Our approach is based on analysis saturation Hölder inequality for We prove in our main result that, p∈(1,∞), real-valued Schatten-p norm a continuous and single-valued function provide an explicit form its computation. For special case p = 1, set-valued; by adding rank constra...