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1. CMB 2014 (vol 58 pp. 174)

Raffoul, Youssef N.
 Periodic Solutions of Almost Linear Volterra Integro-dynamic Equation on Periodic Time Scales Using Krasnoselskii's fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this papers are new for the continuous and discrete time scales. Keywords:Volterra integro-dynamic equation, time scales, Krasnoselsii's fixed point theorem, periodic solutionCategories:45J05, 45D05

2. CMB 2014 (vol 58 pp. 128)

Marković, Marijan
 A Sharp Constant for the Bergman Projection For the Bergman projection operator $P$ we prove that \begin{equation*} \|P\colon L^1(B,d\lambda)\rightarrow B_1\| = \frac {(2n+1)!}{n!}. \end{equation*} Here $\lambda$ stands for the hyperbolic metric in the unit ball $B$ of $\mathbb{C}^n$, and $B_1$ denotes the Besov space with an adequate semi--norm. We also consider a generalization of this result. This generalizes some recent results due to PerÃ¤lÃ¤. Keywords:Bergman projections, Besov spacesCategories:45P05, 47B35

3. CMB 2013 (vol 57 pp. 794)

Fang, Zhong-Shan; Zhou, Ze-Hua
 New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk We give some new characterizations for compactness of weighted composition operators $uC_\varphi$ acting on Bloch-type spaces in terms of the power of the components of $\varphi,$ where $\varphi$ is a holomorphic self-map of the polydisk $\mathbb{D}^n,$ thus generalizing the results obtained by HyvÃ¤rinen and LindstrÃ¶m in 2012. Keywords:weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variablesCategories:47B38, 47B33, 32A37, 45P05, 47G10

4. CMB 2011 (vol 56 pp. 80)

 Vanishing Theorems in Colombeau Algebras of Generalized Functions Using a canonical linear embedding of the algebra ${\mathcal G}^{\infty}(\Omega)$ of Colombeau generalized functions in the space of $\overline{\C}$-valued $\C$-linear maps on the space ${\mathcal D}(\Omega)$ of smooth functions with compact support, we give vanishing conditions for functions and linear integral operators of class ${\mathcal G}^\infty$. These results are then applied to the zeros of holomorphic generalized functions in dimension greater than one. Keywords:Colombeau generalized functions, linear integral operators, generalized holomorphic functionsCategories:32A60, 45P05, 46F30