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1. CMB Online first
New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk |
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 variables Categories:47B38, 47B33, 32A37, 45P05, 47G10 |
2. CMB 2011 (vol 56 pp. 80)
Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity |
Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's
and Schaefer's fixed point theorems are employed in the analysis.
The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions.
We employ Liapunov's direct method to obtain such an a priori bound.
In the process, we compare these theorems in terms of assumptions and outcomes.
Keywords:Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theorem Categories:45D05, 45J05 |
3. CMB 2008 (vol 51 pp. 618)
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 functions Categories:32A60, 45P05, 46F30 |
4. CMB 2008 (vol 51 pp. 372)
Picard's Iterations for Integral Equations of Mixed Hammerstein Type A new semilocal convergence result for the Picard method is presented,
where the main required condition in the contraction mapping principle is relaxed.
Keywords:nonlinear equations in Banach spaces, successive approximations, semilocal convergence theorem, Picard's iteration, Hammerstein integral equations Categories:45G10, 47H99, 65J15 |