This paper addresses the minimal subset selection of antennas achieving designated channel capacity. This is one of the most natural approaches to alleviating the power consumption in MIMO systems, while it is a mathematically challenging nonlinearlyconstrained sparse optimization ( -norm minimization) problem. We present an ef cient algorithmic solution, to this highly combinatorial problem, u...

We prove that a Banach lattice X which does not contain the ln ∞uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology. 1980 Mathematics Subject Classification: Primary 46B03, 46B42.

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

We establish exponential decay in Hölder norm of transfer operators applied to smooth observables uniformly and nonuniformly expanding semiflows with correlations.

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) If the Banach space is weakly ...

where co means the convex hull and the given functions ai(·) : R n → R, i = 1, 2, . . . , k are supposed to satisfy the following assumptions: A(i): ai(·) are twice continuously differentiable, and A(ii): ai(·) are with linear growth: ‖ai(x)‖ ≤ θ(1 + ‖x‖) for some positive θ, where ‖ · ‖ is the Euclidean norm. For any sequence of k elements (f1, f2, . . . , fk) we use the notation {fi} k i=1. D...

In the present paper, we consider nonlinear functional differential inequalities appearing in the theory of boundary value problems (see [1]–[6] and the references therein) and formulate new results on a priori estimates of their solutions satisfying the boundary conditions of periodic type. Let n be a natural number, ω > 0, C([0, ω]) be the space of (n − 1) times continuously differentiable fu...

We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r-times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the n-th minimal errors are bounded by cn−r/d−1+1/p if and only if X is of ...

A Banach spaceX with the property that every absolutely continuousX−valued function is almost everywhere differentiable is said to be a Radon-Nikodym space [7, pp. 217–219] or [2, 13] (see also [3]). For example, every reflexive Banach space (in particular, every Hilbert space) is a Radon-Nikodym space, but the space L∞ [0, 1] of all K−valued, essentially bounded functions defined on the interv...