Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperbolic metric if and only if it has finite Schwarzian norm, thus generalizing a result of B. Schwarz for analytic functions. A numerical bound is obt...

We consider the problem of minimizing the distance ‖f − φ‖Lp(K), where K is a subset of the complex unit circle ∂D and φ ∈ C(K), subject to the constraint that f lies in the Hardy space H(D) and |f | ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extrema...

We investigate here how some results of Hanzon and Ober [6] can be used to obtain reduced order controllers. The idea is to apply the principle of Nehari extension, which generates optimally robust stabilizing controllers, to functions which have multiple maximal singular values. It is well known that in this case the controller has a drop in degree. Using the parametrization of [6], we obtain ...

This paper is dedicated to studying nonstationary homoclinic solutions with the least energy for a class of fractional reaction-diffusion system \begin{document}$ \begin{eqnarray*} \label{1.1} \left\{\begin{array}{lll} \partial_t u+ (-\Delta)^s u+V(x)u+W(x)v = H_v(t, x, u, v), \\ - v + v+V(x)v+W(x)u H_u(t, |u(t, x)|+|v(t, x)|\rightarrow 0, \ \text{as}\ |t|+|x|\rightarrow \infty, \end{array} \ri...

The standard way to obtain explicit formulas for spectral factorization problems for rational transfer functions is to use a minimal realization and then obtain formulae in terms of the generators A, B, C and D. For well-posed linear systems with unbounded generators these formulae will not always be well-defined. Instead, we suggest another approach for the class of well-posed linear systems f...

Problems of Nehari type are studied for matrix valued k-variable almost periodic Wiener functions: Find contractive k-variable almost periodic Wiener functions having prespeciied Fourier coeecients with indices in a given halfspace of R k. We characterize the existence of a solution, give a construction of the solution set, and exhibit a particular solution that has a certain maximizing propert...

Multiple subcarrier modulation (MSM) is an attractive technique for optical wireless communication for high speed applications. The main disadvantage of this scheme is its low average power efficiency which is an analogous problem to the high peak to mean envelope power ratio (PMEPR) of multicarrier signals. In this paper, we consider the achievable average power reduction of MSM signals by usi...

The Grassmannian/Krĕın-space approach to interpolation theory introduced in the 1980s gives a Krĕın-space geometry approach to arriving at the resolvent matrix which parametrizes the set of solutions to a NevanlinnaPick interpolation or Nehari-Takagi best-approximation problem. We review the basics of this approach and then discuss recent extensions to multivariable settings which were not anti...

This paper is concerned with functionals which were introduced by Nehari [8,9] and also discussed by Coffman [2,3] in connection with the study of nonlinear boundary value problems. Their behavior under the Schwarz syitimetrization [12] is studied, and an isoperimetric inequality analogous to that of RayleighFaber-Krahn [12] for the fundamental frequency of a vibrating membrane is derived. v Th...

In this paper we study quasilinear elliptic equations driven by the double phase operator involving a Choquard term of form −Lp,qa(u)+|u|p−2u+a(x)|u|q−2u=∫RNF(y,u)|x−y|μdyf(x,u)inRN,where Lp,qa is given Lp,qa(u)≔div(|∇u|p−2∇u+a(x)|∇u|q−2∇u),u∈W1,H(RN), 0<μ<N, 1<p<N, p<q<p+αpN, 0≤a(⋅)∈C0,α(RN) with α∈(0,1] and f:RN×R→R continuous function that satisfies subcritical growth. Based on Hardy–Littlew...