共查询到20条相似文献,搜索用时 31 毫秒
1.
Let j{\varphi} be an analytic self-map of the unit disk
\mathbbD{\mathbb{D}},
H(\mathbbD){H(\mathbb{D})} the space of analytic functions on
\mathbbD{\mathbb{D}} and
g ? H(\mathbbD){g \in H(\mathbb{D})}. The boundedness and compactness of the operator DCj : H¥ ? Z{DC_\varphi : H^\infty \rightarrow { \mathcal Z}} are investigated in this paper. 相似文献
2.
Amol Sasane 《Complex Analysis and Operator Theory》2012,6(2):465-475
Let
\mathbb Dn:={z=(z1,?, zn) ? \mathbb Cn:|zj| < 1, j=1,?, n}{\mathbb {D}^n:=\{z=(z_1,\ldots, z_n)\in \mathbb {C}^n:|z_j| < 1, \;j=1,\ldots, n\}}, and let
[`(\mathbbD)]n{\overline{\mathbb{D}}^n} denote its closure in
\mathbb Cn{\mathbb {C}^n}. Consider the ring
Cr([`(\mathbbD)]n;\mathbb C) = {f:[`(\mathbbD)]n? \mathbb C:f is continuous and f(z)=[`(f([`(z)]))] (z ? [`(\mathbbD)]n)}C_{\rm r}(\overline{\mathbb{D}}^n;\mathbb {C}) =\left\{f: \overline{\mathbb{D}}^n\rightarrow \mathbb {C}:f \,\, {\rm is \,\, continuous \,\, and}\,\, f(z)=\overline{f(\overline{z})} \;(z\in \overline{\mathbb{D}}^n)\right\} 相似文献
3.
S. S. Gribkova 《Journal of Mathematical Sciences》2010,167(4):506-511
Let x(t),t ? [ 0,1 ] \xi (t),t \in \left[ {0,1} \right] , be a jump Lévy process. By Px {\mathcal{P}_\xi } we denote the law of in the Skorokhod space
\mathbbD {\mathbb{D}} [0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of Px {\mathcal{P}_\xi } -preserving transformations of the space
\mathbbD {\mathbb{D}} [0, 1]. Bibliography: 10 titles. 相似文献
4.
In this paper, we mainly study polynomial generalized Vekua-type equation _boxclose)w=0{p(\mathcal{D})w=0} and polynomial generalized Bers–Vekua equation p(D)w=0{p(\mathcal{\underline{D}})w=0} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}} where D{\mathcal{D}} and D{\mathcal{\underline{D}}} mean generalized Vekua-type operator and generalized Bers–Vekua operator, respectively. Using Clifford algebra, we obtain
the Fischer-type decomposition theorems for the solutions to these equations including
(D-l)kw=0,(D-l)kw=0(k ? \mathbbN){\left(\mathcal{D}-\lambda\right)^{k}w=0,\left(\mathcal {\underline{D}}-\lambda\right)^{k}w=0\left(k\in\mathbb{N}\right)} with complex parameter λ as special cases, which derive the Almansi-type decomposition theorems for iterated generalized
Bers–Vekua equation and polynomial generalized Cauchy–Riemann equation defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}. Making use of the decomposition theorems we give the solutions to polynomial generalized Bers–Vekua equation defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}} under some conditions. Furthermore we discuss inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}, and develop the structure of the solutions to inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}. 相似文献
5.
Let T be a C0–contraction on a separable Hilbert space. We assume that IH − T*T is compact. For a function f holomorphic in the unit disk
\mathbbD{\mathbb{D}} and continuous on
[`(\mathbbD)]\overline{{\mathbb{D}}}, we show that f(T) is compact if and only if f vanishes on
s(T)?\mathbbT\sigma(T)\cap{\mathbb{T}}, where σ(T) is the spectrum of T and
\mathbbT{\mathbb{T}} the unit circle. If f is just a bounded holomorphic function on
\mathbbD{\mathbb{D}}, we prove that f(T) is compact if and only if limn? ¥||Tnf(T)|| = 0\lim\limits_{n\rightarrow \infty}\|T^{n}f(T)\| = 0. 相似文献
6.
The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions
Olli Hyv?rinen Mika Kemppainen Mikael Lindstr?m Antti Rautio Erno Saukko 《Integral Equations and Operator Theory》2012,72(2):151-157
For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCj{uC_\varphi} on the weighted Banach spaces of analytic functions in terms of the analytic function
u \colon \mathbb D ? \mathbb C{u \colon \mathbb D \to \mathbb C} and the nth power of the analytic selfmap j{\varphi} of the open unit disc
\mathbb D{\mathbb D} . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general
radial weights. 相似文献
7.
Let
J:\mathbbR ? \mathbbRJ:\mathbb{R} \to \mathbb{R}
be a nonnegative, smooth compactly supported function such that
ò\mathbbR J(r)dr = 1. \int_\mathbb{R} {J(r)dr = 1.}
We consider the nonlocal diffusion problem
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