Outer operators for the noncommutative symmetric hardy spaces associated with finite subdiagonal algebra

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.     

A Buzano type inequality for two Hermitian forms and applications

A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given.     

Pseudo‐differential operators in a Gelfand–Shilov setting

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes.     

On the symmetry analysis and conservation laws of the (1 + 1)‐dimensional Hénon–Lane–Emden system

We carry out a complete Lie symmetry analysis and Noether symmetry classification of the (1 + 1)‐dimensional H non–Lane–Emden system. It is shown that the principal Lie algebra, which is one dimensional, extends in several cases. It is also shown that four main cases transpire in the Noether classification with respect to the Lagrangian. In addition, conservation laws for the H non–Lane–Emden system are constructed. Furthermore, we briefly discuss the importance and the physical interpretation of these conserved vectors. Copyright © 2016 John Wiley & Sons, Ltd.     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Fundamental solution of the time‐fractional telegraph Dirac operator

In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems.     

Lipschitz continuity ofV-subdifferentials of convex operators

It is proved that theV-subdifferential of a convex operator is locally Lipschitzian on the set of points at which it is continuous and subdifferentiable.Proposition 2.2 was originally stated for Holder continuity ofV-subdifferentials. The author would like to thank J. P. Penot for a very helpful suggestion which led to the present form of this proposition.     

Multilinear forms and measures of dependence between random variables

Based on an idea of Rosenblatt, the methods of interpolation theory are used to establish moment inequalities and equivalence relations for measures of dependence between two or more families of random variables. A couple of “interpolation” theorems proved here appear to be new.     

Alternative characterisations of Lorentz-Karamata spaces

We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.