共查询到20条相似文献,搜索用时 15 毫秒
1.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}Let Ω be a domain in
\mathbbC2{\mathbb{C}^{2}}, and let
p: [(W)\tilde]? \mathbbC2{\pi: \tilde{\Omega}\rightarrow \mathbb{C}^{2}} be its envelope of holomorphy. Also let W¢=p([(W)\tilde]){\Omega'=\pi(\tilde{\Omega})} with
i: W\hookrightarrow W¢{i: \Omega \hookrightarrow \Omega'} the inclusion. We prove the following: if the induced map on fundamental groups i*:p1(W) ? p1(W¢){i_{*}:\pi_{1}(\Omega) \rightarrow \pi_{1}(\Omega')} is a surjection, and if π is a covering map, then Ω has a schlicht envelope of holomorphy. We then relate this to earlier
work of Fornaess and Zame. 相似文献
2.
Rumi Shindo 《Mediterranean Journal of Mathematics》2011,8(1):81-95
Let A, B be uniform algebras. Suppose that A
0, B
0 are subgroups of A
−1, B
−1 that contain exp A, exp B respectively. Let α be a non-zero complex number. Suppose that m, n are non-zero integers and d is the greatest common divisor of m and n. If T : A
0 → B
0 is a surjection with ||T(f)mT(g)n - a||¥ = ||fmgn - a||¥{\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}} for all f,g ? A0{f,g \in A_0}, then there exists a real-algebra isomorphism [(T)\tilde] : A ? B{\tilde{T} : A \rightarrow B} such that [(T)\tilde](f)d = (T(f)/T(1))d{\tilde{T}(f)^d = (T(f)/T(1))^d} for every f ? A0{f \in A_0}. This result leads to the following assertion: Suppose that S
A
, S
B
are subsets of A, B that contain A
−1, B
−1 respectively. If m, n > 0 and a surjection T : S
A
→ S
B
satisfies ||T(f)mT(g)n - a||¥ = ||fmgn - a||¥{\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}} for all f, g ? SA{f, g \in S_A}, then there exists a real-algebra isomorphism [(T)\tilde] : A ? B{\tilde{T} : A \rightarrow B} such that [(T)\tilde](f)d = (T(f)/T(1))d{\tilde{T}(f)^d = (T(f)/T(1))^d} for every f ? SA{f \in S_A}. Note that in these results and elsewhere in this paper we do not assume that T(exp A) = exp B. 相似文献
3.
Dani Szpruch 《The Ramanujan Journal》2011,26(1):45-53
Let
\mathbbF\mathbb{F} be a p-adic field, let χ be a character of
\mathbbF*\mathbb{F}^{*}, let ψ be a character of
\mathbbF\mathbb{F} and let gy-1\gamma_{\psi}^{-1} be the normalized Weil factor associated with a character of second degree. We prove here that one can define a meromorphic
function [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi ,s,\psi) via a similar functional equation to the one used for the definition of the Tate γ-factor replacing the role of the Fourier transform with an integration against y·gy-1\psi\cdot\gamma_{\psi}^{-1}. It turns out that γ and [(g)\tilde]\widetilde{\gamma} have similar integral representations. Furthermore, [(g)\tilde]\widetilde{\gamma} has a relation to Shahidi‘s metaplectic local coefficient which is similar to the relation γ has with (the non-metalpectic) Shahidi‘s local coefficient. Up to an exponential factor, [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi,s,\psi) is equal to the ratio
\fracg(c2,2s,y)g(c,s+\frac12,y)\frac{\gamma(\chi^{2},2s,\psi)}{\gamma(\chi,s+\frac{1}{2},\psi)}. 相似文献
4.
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
5.
In Finsler geometry, minimal surfaces with respect to the Busemann-Hausdorff measure and the Holmes-Thompson measure are called
BH-minimal and HT-minimal surfaces, respectively. In this paper, we give the explicit expressions of BH-minimal and HT-minimal
rotational hypersurfaces generated by plane curves rotating around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski (α, β)-space
(\mathbbVn+1,[(Fb)\tilde]){(\mathbb{V}^{n+1},\tilde{F_b})} , where
\mathbbVn+1{\mathbb{V}^{n+1}} is an (n+1)-dimensional real vector space, [(Fb)\tilde]=[(a)\tilde]f([(b)\tilde]/[(a)\tilde]), [(a)\tilde]{\tilde{F_b}=\tilde{\alpha}\phi(\tilde{\beta}/\tilde{\alpha}), \tilde{\alpha}} is the Euclidean metric, [(b)\tilde]{\tilde{\beta}} is a one form of constant length
b:=||[(b)\tilde]||[(a)\tilde], [(b)\tilde]\sharp{b:=\|\tilde{\beta}\|_{\tilde{\alpha}}, \tilde{\beta}^{\sharp}} is the dual vector of [(b)\tilde]{\tilde{\beta}} with respect to [(a)\tilde]{\tilde{\alpha}} . As an application, we first give the explicit expressions of the forward complete BH-minimal rotational surfaces generated
around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski Randers 3-space
(\mathbbV3,[(a)\tilde]+[(b)\tilde]){(\mathbb{V}^{3},\tilde{\alpha}+\tilde{\beta})} . 相似文献
6.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
7.
Let T = U|T| be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation T = |T|^1/2 U|T|^1/2 is called the Aluthge transformation and Tn means the n-th Aluthge transformation. Similarly, the transformation T(*)=|T*|^1/2 U|T*|&1/2 is called the *-Aluthge transformation and Tn^(*) means the n-th *-Aluthge transformation. In this paper, firstly, we show that T(*) = UV|T^(*)| is the polar decomposition of T(*), where |T|^1/2 |T^*|^1/2 = V||T|^1/2 |T^*|^1/2| is the polar decomposition. Secondly, we show that T(*) = U|T^(*)| if and only if T is binormal, i.e., [|T|, |T^*|]=0, where [A, B] = AB - BA for any operator A and B. Lastly, we show that Tn^(*) is binormal for all non-negative integer n if and only if T is centered, and so on. 相似文献
8.
D. Wolke 《Archiv der Mathematik》2000,74(4):276-281
On the assumption of the truth of the Riemann hypothesis for the Riemann zeta function we construct a class of modified von-Mangoldt functions with slightly better mean value properties than the well known function L\Lambda . For every e ? (0,1/2)\varepsilon \in (0,1/2) there is a [(L)\tilde] : \Bbb N ? \Bbb C\tilde {\Lambda} : \Bbb N \to \Bbb C such that¶ i) [(L)\tilde] (n) = L (n) (1 + O(n-1/4 logn))\tilde {\Lambda} (n) = \Lambda (n) (1 + O(n^{-1/4\,} \log n)) and¶ii) ?n \leqq x [(L)\tilde] (n) (1- [(n)/(x)]) = [(x)/2] + O(x1/4+e) (x \geqq 2).\sum \limits_{n \leqq x} \tilde {\Lambda} (n) \left(1- {{n}\over{x}}\right) = {{x}\over{2}} + O(x^{1/4+\varepsilon }) (x \geqq 2).¶Unfortunately, this does not lead to an improved error term estimation for the unweighted sum ?n \leqq x [(L)\tilde] (n)\sum \limits_{n \leqq x} \tilde {\Lambda} (n), which would be of importance for the distance between consecutive primes. 相似文献
9.
Manuel del Pino Michal Kowalczyk Juncheng Wei Jun Yang 《Geometric And Functional Analysis》2010,20(4):918-957
Let (M,[(g)\tilde]){(\mathcal {M},\tilde{g})} be an N-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen–Cahn equation
e2 D[(g)\tilde] u + (1 - u2 )u = 0 in M,\varepsilon ^2 \Delta _{\tilde g} u \, + \, (1 - u^2 )u\, =\, 0 \quad {\rm{in}} \, \mathcal {M}, 相似文献
10.
Lasha Ephremidze Gigla Janashia Edem Lagvilava 《Journal of Fourier Analysis and Applications》2011,17(5):976-990
It is proved that if positive definite matrix functions (i.e. matrix spectral densities) S
n
, n=1,2,… , are convergent in the L
1-norm, ||Sn-S||L1? 0\|S_{n}-S\|_{L_{1}}\to 0, and ò02plogdetSn(eiq) dq?ò02plogdetS(eiq) dq\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S_{n}(e^{i\theta})\,d\theta\to\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S(e^{i\theta})\,d\theta, then the corresponding (canonical) spectral factors are convergent in L
2, ||S+n-S+||L2? 0\|S^{+}_{n}-S^{+}\|_{L_{2}}\to 0. The formulated logarithmic condition is easily seen to be necessary for the latter convergence to take place. 相似文献
11.
It has been known since the 1970s that the Torelli map M
g
→A
g
, associating to a smooth curve its Jacobian, extends to a regular map from the Deligne–Mumford compactification
[`(\operatorname M)]g\overline {\operatorname {M}}_{g} to the 2nd Voronoi compactification
[`(\operatorname A)]gvor\overline {\operatorname {A}}_{g}^{\mathrm {vor}}. We prove that the extended Torelli map to the perfect cone (1st Voronoi) compactification
[`(\operatorname A)]gperf\overline {\operatorname {A}}_{g}^{\mathrm {perf}} is also regular, and moreover
[`(\operatorname A)]gvor\overline {\operatorname {A}}_{g}^{\mathrm {vor}} and
[`(\operatorname A)]gperf\overline {\operatorname {A}}_{g}^{\mathrm {perf}} share a common Zariski open neighborhood of the image of
[`(\operatorname M)]g\overline {\operatorname {M}}_{g}. We also show that the map to the Igusa monoidal transform (central cone compactification) is not regular for g≥9; this disproves a 1973 conjecture of Namikawa. 相似文献
12.
Martin Reiris 《Annales Henri Poincare》2010,10(8):1559-1604
Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume ${\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)}
13.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2010,20(1):1-12
The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions $f
: {\mathbb{R}}^{2n} \mapsto {\mathbb{C}}_{n}$f
: {\mathbb{R}}^{2n} \mapsto {\mathbb{C}}_{n} of the so called isotonic system
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