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Thu, 18 Jul 2019 07:47:40 +0100FeedCreatorAdvances in Operator Theory
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Feed provided by Advances in Operator Theory. Click to visit.On Zipf-Mandelbrot entropy and 3-convex functions
http://www.aot-math.org/article_82412_8968.html
‎In this paper‎, ‎we present some interesting results related to the bounds of Zipf-Mandelbrot entropy and the $3$-convexity of the function‎. ‎Further‎, ‎we define linear functionals as the non-negative differences of the obtained inequalities and we present mean value theorems for the linear functionals‎. ‎Finally‎, ‎we discuss the n-exponential convexity and the log-convexity of the functions‎ ‎associated with the linear functionals‎.Mon, 30 Sep 2019 20:30:00 +0100Analytic variable exponent Hardy spaces
http://www.aot-math.org/article_83079_8968.html
We introduce a variable exponent version of the Hardy space of analytic functions on the unit disk, we show some properties of the space, and give an example of a variable exponent $p(cdot)$ that satisfies the $log$-H"older condition, and $H^{p(cdot)}neq H^q$ for every constant exponent $1<q<infty$. We also consider the variable exponent version of the Hardy space on the upper-half plane.Mon, 30 Sep 2019 20:30:00 +0100Riesz transform and fractional integral operators generated by non-degenerate elliptic ...
http://www.aot-math.org/article_83168_8968.html
‎The Morrey boundedness‎ ‎is proved‎ ‎for the Riesz transform and the inverse operator‎ ‎of the non-degenerate elliptic differential operator of divergence form‎ ‎generated by a vector-function in $(L^infty)^{n^2}$‎, ‎and for the inverse operator of the Schr"{o}dinger operators whose non-negative potentials satisfy a certain integrability condition‎. ‎In this note‎, ‎our result is not obtained directly from the estimates of integral formula‎, ‎which reflects the fact that the solution of the Kato conjecture‎ ‎did not use any integral expression of the operators‎. ‎One of the important tools in the proof‎ ‎is the decomposition of the functions in Morrey spaces‎ ‎based on the elliptic differential operators in question‎. ‎In some special cases‎ ‎where the integral kernel comes into play‎, ‎the boundedness property of the Littlewood--Paley operator‎ ‎was already obtained by Gong‎. ‎So‎, ‎the main novelties of this paper‎ ‎are the decomposition results associated with elliptic differential operators‎ ‎and the result in the case where the explicit formula of the integral kernel of the heat semigroup‎ ‎is unavailable.Mon, 30 Sep 2019 20:30:00 +0100On $m$-convexity of set-valued functions
http://www.aot-math.org/article_83544_8968.html
‎‎We introduce the notion of an $m$-convex set-valued‎ ‎function and study some properties of this class of functions‎. ‎Several characterizations are given as well as certain algebraic‎ ‎properties and examples‎. ‎Finally‎, ‎an inclusion of Jensen type is‎ ‎presented jointly with a sandwich type theorem‎.Mon, 30 Sep 2019 20:30:00 +0100A trick for investigation of near-martingales in quantum probability spaces
http://www.aot-math.org/article_85669_8968.html
‎‎In this paper‎, ‎we introduce near-martingales in the setting of quantum probability spaces and present a trick for investigating some of their properties‎. ‎For instance‎, ‎we give a near-martingale analogous result of the fact that the space of all bounded $L^p$-martingales‎, ‎equipped with the norm $|cdot|_p$‎, ‎is isometric to $L^p(mathfrak{M})$ for $p>1$‎. ‎We also present Doob and Riesz decompositions for the near-submartingale and provide Gundy's decomposition for $L^1$-bounded near-martingales‎. ‎In addition‎, ‎the interrelation between near-martingales and the instantly independence is studied.Mon, 30 Sep 2019 20:30:00 +0100Invertibility of Toeplitz operators with polyanalytic symbols
http://www.aot-math.org/article_85693_8968.html
‎For a class of continuous functions including complex polynomials in $z,bar{z},$ we show that‎ ‎the corresponding Toeplitz operator on the Bergman space of the unit disc‎ ‎can be expressed as a quotient of certain differential operators with holomorphic coefficients‎. ‎This enables us to obtain several nontrivial operator theoretic results about such Toeplitz operators‎, ‎including a new criterion for invertibility of a Toeplitz operator for a class of harmonic symbols‎.Mon, 30 Sep 2019 20:30:00 +0100Approximate and trajectory controllability of fractional neutral differential equation
http://www.aot-math.org/article_85816_8968.html
‎In this article‎, ‎we study a new class of fractional neutral differential control system with non-instantaneous impulses and state-dependent delay‎. ‎The resolvent family and Krasnoselskii's fixed point theorem are utilized to examine the approximate controllability outcomes for the proposed system‎. ‎Further‎, ‎we derive the trajectory controllability outcomes for the proposed fractional control system‎. ‎Finally‎, ‎the main results are validated with the aid of an example‎.Mon, 30 Sep 2019 20:30:00 +0100Three solutions for a Kirchhoff type problem involving nonlocal fractional $p$-Laplacian
http://www.aot-math.org/article_86159_8968.html
‎In this paper‎, ‎using the three critical points theorem‎ ‎we obtain the existence of three weak solutions for‎ ‎a Kirchhoff type problem involving‎ ‎the nonlocal fractional $p$-Laplacian operator in a fractional Sobolev space‎, ‎with homogeneous Dirichlet boundary conditions.‎Mon, 30 Sep 2019 20:30:00 +0100Extension of the truncated bi-indexed weighted shifts, recursiveness and subnormality
http://www.aot-math.org/article_86937_8968.html
‎In this paper, we build a process in order to extend the truncated weighted shift‎, ‎using techniques of the bi-indexed recursive sequences‎. ‎We apply this process to solve the subnormality of $2$-variable weighted shifts‎, ‎whose associated moment sequence is a bi-indexed recursive sequence‎. ‎Notably‎, ‎we detail the case of the truncated $2$-variable weighted shift $Tequiv(T_1‎, ‎T_2)$ of order $(2,2)$‎.Mon, 30 Sep 2019 20:30:00 +0100An ultrapower construction of the multiplier algebra of a $C^*$-algebra and an application to ...
http://www.aot-math.org/article_87364_8968.html
‎Using ultrapowers of $C^*$-algebras we provide a new construction of the multiplier algebra of a $C^*$-algebra‎. ‎This extends the work of Avsec and Goldbring [Houston J‎. ‎Math.‎, ‎to appear‎, ‎arXiv:1610.09276]‎. ‎to the setting of noncommutative and non separable $C^*$-algebras‎. ‎We also extend their work to give a new proof of the fact that groups that act transitively on locally finite trees with boundary amenable stabilizers are boundary amenable‎.Mon, 30 Sep 2019 20:30:00 +0100