共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
3.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
4.
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
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.
Erik Talvila 《Journal of Fourier Analysis and Applications》2012,18(1):27-44
Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional
derivative of a continuous function. This space of distributions is denoted
Ac(\mathbbT){\mathcal{A}}_{c}(\mathbb{T}) and is a Banach space under the Alexiewicz norm,
||f||\mathbbT=sup|I| £ 2p|òI f|\|f\|_{\mathbb{T}}=\sup_{|I|\leq2\pi}|\int_{I} f|, the supremum being taken over intervals of length not exceeding 2π. It contains the periodic functions integrable in the sense of Lebesgue and Henstock–Kurzweil. Many of the properties of
L
1 Fourier series continue to hold for this larger space, with the L
1 norm replaced by the Alexiewicz norm. The Riemann–Lebesgue lemma takes the form [^(f)](n)=o(n)\hat{f}(n)=o(n) as |n|→∞. The convolution is defined for
f ? Ac(\mathbbT)f\in{\mathcal{A}}_{c}(\mathbb{T}) and g a periodic function of bounded variation. The convolution commutes with translations and is commutative and associative.
There is the estimate
||f*g||¥ £ ||f||\mathbbT ||g||BV\|f\ast g\|_{\infty}\leq\|f\|_{\mathbb{T}} \|g\|_{\mathcal{BV}}. For
g ? L1(\mathbbT)g\in L^{1}(\mathbb{T}),
||f*g||\mathbbT £ ||f||\mathbb T ||g||1\|f\ast g\|_{\mathbb{T}}\leq\|f\|_{\mathbb {T}} \|g\|_{1}. As well, [^(f*g)](n)=[^(f)](n) [^(g)](n)\widehat{f\ast g}(n)=\hat{f}(n) \hat{g}(n). There are versions of the Salem–Zygmund–Rudin–Cohen factorization theorem, Fejér’s lemma and the Parseval equality. The
trigonometric polynomials are dense in
Ac(\mathbbT){\mathcal{A}}_{c}(\mathbb{T}). The convolution of f with a sequence of summability kernels converges to f in the Alexiewicz norm. Let D
n
be the Dirichlet kernel and let
f ? L1(\mathbbT)f\in L^{1}(\mathbb{T}). Then
||Dn*f-f||\mathbbT?0\|D_{n}\ast f-f\|_{\mathbb{T}}\to0 as n→∞. Fourier coefficients of functions of bounded variation are characterized. The Appendix contains a type of Fubini theorem. 相似文献
7.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2010,62(2):241-258
It is shown that if a point x
0 ∊ ℝ
n
, n ≥ 3, is an essential isolated singularity of an open discrete Q-mapping f : D →
[`(\mathbb Rn)] \overline {\mathbb {R}^n} , B
f
is the set of branch points of f in D; and a point z
0 ∊
[`(\mathbb Rn)] \overline {\mathbb {R}^n} is an asymptotic limit of f at the point x
0; then, for any neighborhood U containing the point x
0; the point z
0 ∊ [`(f( Bf ?U ))] \overline {f\left( {B_f \cap U} \right)} provided that the function Q has either a finite mean oscillation at the point x
0 or a logarithmic singularity whose order does not exceed n − 1: Moreover, for n ≥ 2; under the indicated conditions imposed on the function Q; every point of the set
[`(\mathbb Rn)] \overline {\mathbb {R}^n} \ f(D) is an asymptotic limit of f at the point x
0. For n ≥ 3, the following relation is true:
[`(\mathbbRn )] \f( D ) ì [`(f Bf )] \overline {\mathbb{R}^n } \backslash f\left( D \right) \subset \overline {f\,B_f } . In addition, if ¥ ? f( D ) \infty \notin f\left( D \right) , then the set f
B
f
is infinite and x0 ? [`(Bf )] x_0 \in \overline {B_f } . 相似文献
8.
Sorin G. Gal 《Complex Analysis and Operator Theory》2012,6(2):515-527
Attaching to a compact disk
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} in the quaternion field
\mathbbH{\mathbb{H}} and to some analytic function in Weierstrass sense on
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} the so-called q-Bernstein operators with q ≥ 1, Voronovskaja-type results with quantitative upper estimates are proved. As applications, the exact orders of approximation
in
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} for these operators, namely
\frac1n{\frac{1}{n}} if q = 1 and
\frac1qn{\frac{1}{q^{n}}} if q > 1, are obtained. The results extend those in the case of approximation of analytic functions of a complex variable in disks
by q-Bernstein operators of complex variable in Gal (Mediterr J Math 5(3):253–272, 2008) and complete the upper estimates obtained for q-Bernstein operators of quaternionic variable in Gal (Approximation by Complex Bernstein and Convolution-Type Operators, 2009; Adv Appl Clifford Alg, doi:, 2011). 相似文献
9.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(1):84-97
For open discrete mappings
f:D\{ b } ? \mathbbR3 f:D\backslash \left\{ b \right\} \to {\mathbb{R}^3} of a domain
D ì \mathbbR3 D \subset {\mathbb{R}^3} satisfying relatively general geometric conditions in D \ {b} and having an essential singularity at a point
b ? \mathbbR3 b \in {\mathbb{R}^3} , we prove the following statement: Let a point y
0 belong to
[`(\mathbbR3)] \f( D\{ b } ) \overline {{\mathbb{R}^3}} \backslash f\left( {D\backslash \left\{ b \right\}} \right) and let the inner dilatation K
I
(x, f) and outer dilatation K
O
(x, f) of the mapping f at the point x satisfy certain conditions. Let B
f
denote the set of branch points of the mapping f. Then, for an arbitrary neighborhood V of the point y
0, the set V ∩ f(B
f
) cannot be contained in a set A such that g(A) = I, where
I = { t ? \mathbbR:| t | < 1 } I = \left\{ {t \in \mathbb{R}:\left| t \right| < 1} \right\} and
g:U ? \mathbbRn g:U \to {\mathbb{R}^n} is a quasiconformal mapping of a domain
U ì \mathbbRn U \subset {\mathbb{R}^n} such that A ⊂ U. 相似文献
10.
Let M be
(2n-1)\mathbbCP2#2n[`(\mathbbCP)]2(2n-1)\mathbb{CP}^{2}\#2n\overline{\mathbb{CP}}{}^{2} for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is
\mathbbCP2#4[`(\mathbbCP)]2\mathbb{CP}{}^{2}\#4\overline {\mathbb{CP}}{}^{2} or
3\mathbbCP2#k[`(\mathbbCP)]23\mathbb{CP}{}^{2}\#k\overline{\mathbb{CP}}{}^{2} for k=6,8,10. 相似文献
11.
Paul D. Nelson 《The Ramanujan Journal》2012,27(2):235-284
Let
\mathbbF\mathbb{F} be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on
\operatornameGL2/\mathbbF\operatorname{GL}_{2}/\mathbb{F} of weight
(k1,?,k[\mathbbF:\mathbbQ])(k_{1},\ldots,k_{[\mathbb{F}:\mathbb{Q}]}), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as
max(k1,?,k[\mathbbF:\mathbbQ]) ? ¥\max(k_{1},\ldots,k_{[\mathbb{F}:\mathbb{Q}]}) \rightarrow \infty. 相似文献
12.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
13.
Consider j = f +[`(g)]\varphi = f + \overline {g}, where f and g are polynomials, and let TjT_{\varphi} be the Toeplitz operators with the symbol j\varphi. It is known that if TjT_{\varphi} is hyponormal then |f¢(z)|2 3 |g¢(z)|2|f'(z)|^{2} \geq |g'(z)|^{2} on the unit circle in the complex plane. In this paper, we show that it is also a necessary and sufficient condition under
certain assumptions. Furthermore, we present some necessary conditions for the hyponormality of TjT_{\varphi} on the weighted Bergman space, which generalize the results of I. S. Hwang and J. Lee. 相似文献
14.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2012,63(8):1298-1305
The paper is devoted to the investigation of topological properties of space mappings. It is shown that orientation-preserving
mappings
f:D ?[`(\mathbbRn)] f:D \to \overline {{\mathbb{R}^n}} in a domain
D ì \mathbbRn D \subset {\mathbb{R}^n} , n ≥ 2; which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f (D), e.g., if Q has finite mean oscillation at an arbitrary point y
0 ∈ f (D). 相似文献
15.
Yong-Kum Cho Sunggeum Hong Joonil Kim Chan Woo Yang 《Integral Equations and Operator Theory》2009,65(4):485-528
Given
W ì \mathbbZ+3\Omega \subset {\mathbb{Z}}_{+}^{3}, we discuss a necessary and sufficient condition that the triple Hilbert transform associated with any polynomial of the
form ($t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m$t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m) is bounded in
Lp(\mathbbR4)L^p({\mathbb{R}}^4). 相似文献
16.
Vladimir A. Borovikov Francisco Javier Mendoza 《Journal of Fourier Analysis and Applications》2002,8(4):399-406
We study the pointwise convergence problem for the inverse Fourier transform of piecewise smooth functions, i.e., whether SrD f (\bx) ? f (\bx)S_{\rho D} f (\bx) \to f (\bx) as r? ¥\rho \to \infty . r? ¥\rho \to \infty . Here for \bx,\bxi ? \Rn\bx,\bxi \in \Rn SrDf(\bmx)=\dsf1(2p)n/2\intlirD [^(f)](\bxi) e\dst iá\bmx,\bxi? d\bxi . S_{\rho D}f(\bm{x})=\dsf1{(2\pi)^{n/2}}\intli_{\rho D} \widehat{f}(\bxi) e^{\dst i\langle\bm{x},\bxi\rangle} d\bxi~. is the partial sum operator using a convex and open set DD containing the origin, and rD={ r\bxi:\bxi ? D }\rho D=\left\{ \rho \bxi:\bxi\in D \right\}. 相似文献
17.
B. Enriquez 《Selecta Mathematica, New Series》2001,7(3):321-407
To any field
\Bbb K \Bbb K of characteristic zero, we associate a set
(\mathbbK) (\mathbb{K}) and a group
G0(\Bbb K) {\cal G}_0(\Bbb K) . Elements of
(\mathbbK) (\mathbb{K}) are equivalence classes of families of Lie polynomials subject to associativity relations. Elements of
G0(\Bbb K) {\cal G}_0(\Bbb K) are universal automorphisms of the adjoint representations of Lie bialgebras over
\Bbb K \Bbb K . We construct a bijection between
(\mathbbK)×G0(\Bbb K) (\mathbb{K})\times{\cal G}_0(\Bbb K) and the set of quantization functors of Lie bialgebras over
\Bbb K \Bbb K . This construction involves the following steps.? 1) To each element v \varpi of
(\mathbbK) (\mathbb{K}) , we associate a functor
\frak a?\operatornameShv(\frak a) \frak a\mapsto\operatorname{Sh}^\varpi(\frak a) from the category of Lie algebras to that of Hopf algebras;
\operatornameShv(\frak a) \operatorname{Sh}^\varpi(\frak a) contains
U\frak a U\frak a .? 2) When
\frak a \frak a and
\frak b \frak b are Lie algebras, and
r\frak a\frak b ? \frak a?\frak b r_{\frak a\frak b} \in\frak a\otimes\frak b , we construct an element
?v (r\frak a\frak b) {\cal R}^{\varpi} (r_{\frak a\frak b}) of
\operatornameShv(\frak a)?\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak a)\otimes\operatorname{Sh}^\varpi(\frak b) satisfying quasitriangularity identities; in particular,
?v(r\frak a\frak b) {\cal R}^\varpi(r_{\frak a\frak b}) defines a Hopf algebra morphism from
\operatornameShv(\frak a)* \operatorname{Sh}^\varpi(\frak a)^* to
\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak b) .? 3) When
\frak a = \frak b \frak a = \frak b and
r\frak a ? \frak a?\frak a r_\frak a\in\frak a\otimes\frak a is a solution of CYBE, we construct a series
rv(r\frak a) \rho^\varpi(r_\frak a) such that
?v(rv(r\frak a)) {\cal R}^\varpi(\rho^\varpi(r_\frak a)) is a solution of QYBE. The expression of
rv(r\frak a) \rho^\varpi(r_\frak a) in terms of
r\frak a r_\frak a involves Lie polynomials, and we show that this expression is unique at a universal level. This step relies on vanishing
statements for cohomologies arising from universal algebras for the solutions of CYBE.? 4) We define the quantization of a
Lie bialgebra
\frak g \frak g as the image of the morphism defined by ?v(rv(r)) {\cal R}^\varpi(\rho^\varpi(r)) , where
r ? \mathfrakg ?\mathfrakg* r \in \mathfrak{g} \otimes \mathfrak{g}^* .<\P> 相似文献
18.
In this paper we develop a new weak convergence and compact embedding method to study the existence and uniqueness of the
Lr2p(\mathbbRd;\mathbbR1)×Lr2(\mathbbRd;\mathbbRd)L_{\rho}^{2p}({\mathbb{R}^{d}};{\mathbb{R}^{1}})\times L_{\rho}^{2}({\mathbb{R}^{d}};{\mathbb{R}^{d}}) valued solution of backward stochastic differential equations with p-growth coefficients. Then we establish the probabilistic representation of the weak solution of PDEs with p-growth coefficients via corresponding BSDEs. 相似文献
19.
Ilham A. Aliev 《Integral Equations and Operator Theory》2009,65(2):151-167
We introduce new potential type operators Jab = (E+(-D)b/2)-a/bJ^{\alpha}_{\beta} = (E+(-\Delta)^{\beta/2})^{-\alpha/\beta}, (α > 0, β > 0), and bi-parametric scale of function spaces
Hab, p(\mathbbRn)H^{\alpha}_{\beta , p}({\mathbb{R}}^n) associated with Jαβ. These potentials generalize the classical Bessel potentials (for β = 2), and Flett potentials (for β = 1). A characterization
of the spaces
Hab, p(\mathbbRn)H^{\alpha}_{\beta, p}({\mathbb{R}}^n) is given with the aid of a special wavelet–like transform associated with a β-semigroup, which generalizes the well-known
Gauss-Weierstrass semigroup (for β = 2) and the Poisson one (for β = 1). 相似文献
20.
Matteo Dalla Riva Massimo Lanza de Cristoforis 《Complex Analysis and Operator Theory》2011,5(3):811-833
Let Ω
i
and Ω
o
be two bounded open subsets of
\mathbbRn{{\mathbb{R}}^{n}} containing 0. Let G
i
be a (nonlinear) map from
?Wi×\mathbbRn{\partial\Omega^{i}\times {\mathbb{R}}^{n}} to
\mathbbRn{{\mathbb{R}}^{n}} . Let a
o
be a map from ∂Ω
o
to the set
Mn(\mathbbR){M_{n}({\mathbb{R}})} of n × n matrices with real entries. Let g be a function from ∂Ω
o
to
\mathbbRn{{\mathbb{R}}^{n}} . Let γ be a positive valued function defined on a right neighborhood of 0 in the real line. Let T be a map from
]1-(2/n),+¥[×Mn(\mathbbR){]1-(2/n),+\infty[\times M_{n}({\mathbb{R}})} to
Mn(\mathbbR){M_{n}({\mathbb{R}})} . Then we consider the problem
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