共查询到20条相似文献,搜索用时 46 毫秒
1.
Min Ho Lee 《Monatshefte für Mathematik》2004,78(4):187-196
Let
t: D ?D¢\tau: {\cal D} \rightarrow{\cal D}^\prime
be an equivariant holomorphic map of symmetric domains associated to a homomorphism
r: \Bbb G ?\Bbb G¢{\bf\rho}: {\Bbb G} \rightarrow{\Bbb G}^\prime
of semisimple algebraic groups defined over
\Bbb Q{\Bbb Q}
. If
G ì \Bbb G (\Bbb Q)\Gamma\subset {\Bbb G} ({\Bbb Q})
and
G¢ ì \Bbb G¢(\Bbb Q)\Gamma^\prime \subset {\Bbb G}^\prime ({\Bbb Q})
are torsion-free arithmetic subgroups with
r (G) ì G¢{\bf\rho} (\Gamma) \subset \Gamma^\prime
, the map G\D ?G¢\D¢\Gamma\backslash {\cal D} \rightarrow\Gamma^\prime \backslash {\cal D}^\prime
of arithmetic varieties and the rationality of D{\cal D}
and
D¢{\cal D}^\prime
as well as the commensurability groups of
s ? Aut (\Bbb C)\sigma \in {\rm Aut} ({\Bbb C})
determines a conjugate equivariant holomorphic map
ts: Ds ?D¢s\tau^\sigma: {\cal D}^\sigma \rightarrow{\cal D}^{\prime\sigma}
of fs: (G\D)s ?(G¢\D¢)s\phi^\sigma: (\Gamma\backslash {\cal D})^\sigma \rightarrow(\Gamma^\prime \backslash {\cal D}^\prime)^\sigma
of . We prove that is rational if is rational. 相似文献
2.
P. Biran 《Geometric And Functional Analysis》2001,11(3):407-464
We prove that every symplectic Kähler manifold (M;W) (M;\Omega) with integral [W] [\Omega] decomposes into a disjoint union (M,W) = (E,w0) \coprod D (M,\Omega) = (E,\omega_0) \coprod \Delta , where (E,w0) (E,\omega_0) is a disc bundle endowed with a standard symplectic form w0 \omega_0 and D \Delta is an isotropic CW-complex. We perform explicit computations of this decomposition on several examples.¶As an application we establish the following symplectic intersection phenomenon: There exist symplectically irremovable intersections between contractible domains and Lagrangian submanifolds. For example, we prove that every symplectic embedding j:B2n(l) ? \Bbb CPn \varphi:B^{2n}(\lambda) \to {\Bbb C}P^n of a ball of radius l2 3 1/2 \lambda^2 \ge 1/2 must intersect the standard Lagrangian real projective space \Bbb RPn ì \Bbb CPn {\Bbb R}P^n \subset {\Bbb C}P^n . 相似文献
3.
M. Hasson 《Archiv der Mathematik》2001,76(4):283-291
Let W ì \Bbb Rn\Omega \subset {\Bbb R}^n be a smooth domain and let u ? C0(W).u \in C^0(\Omega ). A classical result of potential theory states that¶¶-òSr([`(x)]) u(x)ds(x)=u([`(x)])-\kern-5mm\int\limits _{S_{r}(\bar x)} u(x)d\sigma (x)=u(\bar x)¶¶for every [`(x)] ? W\bar x\in \Omega and r > 0r>0 if and only if¶¶Du=0 in W.\Delta u=0 \hbox { in } \Omega.¶¶Here -òSr([`(x)]) u(x)ds(x)-\kern-5mm\int\limits _{S_{r}(\bar x)} u(x)d\sigma (x) denotes the average of u on the sphere Sr([`(x)])S_r(\bar x) of center [`(x)]\bar x and radius r. Our main result, which is a "localized" version of the above result, states:¶¶Theorem. Let u ? W2,1(W)u\in W^{2,1}(\Omega ) and let x ? Wx\in \Omega be a Lebesgue point of Du\Delta u such that¶¶-òSr([`(x)]) u d s- a = o(r2)-\kern-5mm\int\limits _{S_{r}(\bar x)} u d \sigma - \alpha =o(r^2)¶¶for some a ? \Bbb R\alpha \in \Bbb R and all sufficiently small r > 0.r>0. Then¶¶Du(x)=0.\Delta u(x)=0. 相似文献
4.
Gerd Herzog 《Archiv der Mathematik》2001,77(3):215-221
Let f ? C(\Bbb Rn,\Bbb Rn) f\in C(\Bbb R^n,\Bbb R^n) be quasimonotone increasing such that Y(f(y)-f(x)) £ -c Y(y-x) (x << y) \Psi (f(y)-f(x)) \!\le -c \Psi (y-x) (x\ll y) for a linear and strictly positive functional Y \Psi and c > 0. We prove that f is a homeomorphism with decreasing and Lipschitz continuous inverse and we prove the global asymptotic stability of the equilibrium solution of x¢=f(x) x'=f(x) . 相似文献
5.
In [C.K. Chui and X.L. Shi, Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal., 24 (1993), 263–277], the authors proved that if
{eimbxg(x-na): m,n ? \Bbb Z}\{e^{imbx}g(x-na): m,n\in{\Bbb Z}\}
is a Gabor frame for
L2(\Bbb R)L^2({\Bbb R})
with frame bounds A and B, then the following two inequalities hold:
A £ \frac2pb?n ? \Bbb Z|g(x-na)|2 £ B, a.e.A\le \frac{2\pi}{b}\sum_{n\in{\Bbb Z}}\vert g(x-na)\vert^2\le B, \quad a.e.
and
A £ \frac1a?m ? \Bbb Z|[^(g)](w-mb)|2 £ B, a.e.A\le \frac{1}{a}\sum_{m\in{\Bbb Z}}\vert \hat{g}(\omega-mb)\vert^2\le B, \quad a.e.
. In this paper, we show that similar inequalities hold for multi-generated irregular Gabor frames of the form
è1 £ k £ r{eiáx, l?gk(x-m): m ? Dk, l ? Lk }\bigcup_{1\le k\le r}\{e^{i\langle x, \lambda\rangle}g_{k}(x-\mu):\, \mu\in \Delta_k, \lambda\in\Lambda_k \}
, where Δ
k
and Λ
k
are arbitrary sequences of points in
\Bbb Rd{\Bbb R}^d
and
gk ? L2(\Bbb Rd)g_k\in{L^2{(\Bbb R}^d)}
, 1 ≤ k ≤ r. 相似文献
6.
B. Green 《Geometric And Functional Analysis》2002,12(3):584-597
We prove several results concerning arithmetic progressions in sets of integers. Suppose, for example, that a \alpha and b \beta are positive reals, that N is a large prime and that C,D í \Bbb Z/N\Bbb Z C,D \subseteq {\Bbb Z}/N{\Bbb Z} have sizes gN \gamma N and dN \delta N respectively. Then the sumset C + D contains an AP of length at least ec ?{log} N e^{c \sqrt{\rm log} N} , where c > 0 depends only on g \gamma and d \delta . In deriving these results we introduce the concept of hereditary non-uniformity (HNU) for subsets of \Bbb Z/N\Bbb Z {\Bbb Z}/N{\Bbb Z} , and prove a structural result for sets with this property. 相似文献
7.
Bruno Franchi Maria Carla Tesi 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(4):363-387
In this paper we present homogenization results for elliptic degenerate differential equations describing strongly anisotropic media. More precisely, we study the limit as e? 0 \epsilon \to 0 of the following Dirichlet problems with rapidly oscillating periodic coefficients:¶¶ . \cases {{ -div(\alpha(\frac{x}{\epsilon}}, \nabla u) A(\frac{x}{\epsilon}) \nabla u) = f(x) \in L^{\infty}(\Omega) \atop u = 0 su \eth\Omega\ } ¶¶where, p > 1, a: \Bbb Rn ×\Bbb Rn ? \Bbb R, a(y,x) ? áA(y)x,x?p/2-1, A ? Mn ×n(\Bbb R) p>1, \quad \alpha : \Bbb R^n \times \Bbb R^n \to \Bbb R, \quad \alpha(y,\xi) \approx \langle A(y)\xi,\xi \rangle ^{p/2-1}, A \in M^{n \times n}(\Bbb R) , A being a measurable periodic matrix such that At(x) = A(x) 3 0A^t(x) = A(x) \ge 0 almost everywhere.¶¶The anisotropy of the medium is described by the following structure hypothesis on the matrix A:¶¶l2/p(x) |x|2 £ áA(x)x,x? £ L 2/p(x) |x|2, \lambda^{2/p}(x) |\xi|^2 \leq \langle A(x)\xi,\xi \rangle \leq \Lambda ^{2/p}(x) |\xi|^2, ¶¶where the weight functions l \lambda and L \Lambda (satisfying suitable summability assumptions) can vanish or blow up, and can also be "moderately" different. The convergence to the homogenized problem is obtained by a classical compensated compactness argument, that had to be extended to two-weight Sobolev spaces. 相似文献
8.
Many families of parametrized Thue equations over number fields have been solved recently. In this paper we consider for the
first time a family of Thue equations over a polynomial ring. In particular, we calculate all solutions of
X(X-Y)(X-(T+x)Y)+Y3=1+xT(1-T)X(X-Y)(X-(T+\xi)Y)+Y^3=1+\xi T(1-T)
over
\Bbb C[T]{\Bbb C}[T]
for all
x ? \Bbb C\xi\in{\Bbb C}
. 相似文献
9.
10.
Let
W í \Bbb C\Omega \subseteq {\Bbb C}
be a simply connected domain in
\Bbb C{\Bbb C}
, such that
{¥} è[ \Bbb C \[`(W)]]\{\infty\} \cup [ {\Bbb C} \setminus \bar{\Omega}]
is connected. If g is holomorphic in Ω and every derivative of g extends continuously on
[`(W)]\bar{\Omega}
, then we write g ∈ A∞ (Ω). For g ∈ A∞ (Ω) and
z ? [`(W)]\zeta \in \bar{\Omega}
we denote
SN (g,z)(z) = ?Nl=0\fracg(l) (z)l ! (z-z)lS_N (g,\zeta )(z)= \sum^{N}_{l=0}\frac{g^{(l)} (\zeta )}{l !} (z-\zeta )^l
. We prove the existence of a function f ∈ A∞(Ω), such that the following hold:
相似文献
i) | There exists a strictly increasing sequence μn ∈ {0, 1, 2, …}, n = 1, 2, …, such that, for every pair of compact sets Γ, Δ ⊂ [`(W)]\bar{\Omega} and every l ∈ {0, 1, 2, …} we have supz ? G supw ? D \frac?l?wl Smn ( f,z) (w)-f(l)(w) ? 0, as n ? + ¥ and\sup_{\zeta \in \Gamma} \sup_{w \in \Delta} \frac{\partial^l}{\partial w^l} S_{\mu_ n} (\,f,\zeta) (w)-f^{(l)}(w) \rightarrow 0, \hskip 7.8pt {\rm as}\,n \rightarrow + \infty \quad {\rm and} |
ii) | For every compact set K ì \Bbb CK \subset {\Bbb C} with K?[`(W)] = ?K\cap \bar{\Omega} =\emptyset and Kc connected and every function h: K? \Bbb Ch: K\rightarrow {\Bbb C} continuous on K and holomorphic in K0, there exists a subsequence { m¢n }¥n=1\{ \mu^\prime _n \}^{\infty}_{n=1} of {mn }¥n=1\{\mu_n \}^{\infty}_{n=1} , such that, for every compact set L ì [`(W)]L \subset \bar{\Omega} we have supz ? L supz ? K Sm¢n ( f,z)(z)-h(z) ? 0, as n? + ¥.\sup_{\zeta \in L} \sup_{z\in K} S_{\mu^\prime _n} (\,f,\zeta )(z)-h(z) \rightarrow 0, \hskip 7.8pt {\rm as} \, n\rightarrow + \infty . |
11.
Another logarithmic functional equation 总被引:1,自引:0,他引:1
K. J. Heuvers 《Aequationes Mathematicae》1999,58(3):260-264
Summary. Let f : ]0,¥[? \Bbb R f :\,]0,\infty[\to \Bbb R be a real valued function on the set of positive reals. The functional equations¶¶f(x + y) - f(x) - f(y) = f(x-1 + y-1) f(x + y) - f(x) - f(y) = f(x^{-1} + y^{-1}) ¶and¶f(xy) = f(x) + f(y) f(xy) = f(x) + f(y) ¶are equivalent to each other. 相似文献
12.
Josefina Alvarez Magali Folch-Gabayet Salvador Pérez-Esteva 《Journal of Fourier Analysis and Applications》2001,7(1):49-62
The purpose of this article is to study the Hilbert space W2\mathcal{ W}^2 consisting of all solutions of the Helmholtz equation Du+u=0\Delta u+u=0 in
\BbbR2\Bbb{R}^2 that are the image under the Fourier transform of L2L^2 densities in the unit circle. We characterize this space as a close subspace of the Hilbert space H2\mathcal{ H}^2 of all functions belonging to L2( | x | -3dx) L^2( | x | ^{-3}dx) jointly with their angular and radial derivatives, in the complement of the unit disk in
\BbbR2\Bbb{R}^2. We calculate the reproducing kernel of W2\mathcal{ W}^2 and study its reproducing properties in the corresponding spaces Hp\mathcal{H}^p, for $p>1$p>1. 相似文献
13.
For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq Sn-1\mathbf{S}^{n-1}, Ha(W)H^{\alpha }(\Omega ) is defined as the C2-C^{2}-solutions of Dau=0\Delta _{\alpha }u=0; where Da=Ds+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and Ds\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in Ha(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented. 相似文献
14.
In this paper we study density properties of the Hankel translations of certain positive definite (in the Hankel sense) functions on (0,¥)(0,\infty ). The density is understood in a Fréchet space of smooth functions on (0,¥)(0,\infty ) whose topology is defined by seminorms involving the Bessel operator x-2m-1Dx2m+1Dx^{-2\mu -1}Dx^{2\mu +1}D. 相似文献
15.
Assume that {Sn}1¥ \{S_n\}_1^\infty is a sequence of automorphisms of the open unit disk
\Bbb D{\Bbb D} and that {Tn}1¥\{T_n\}_1^\infty is a sequence of linear differential operators with constant coefficients, both of them satisfying suitable conditions. We prove that for certain spaces X of holomorphic functions in the open unit disk, the set of functions f ? Xf \in X such that
{(Tn f) °Sn: n ? \Bbb N}\{(T_n\,f) \circ S_n: \, n \in {\Bbb N}\} is dense in
H(\Bbb D)H({\Bbb D}) is residual in X. This extends the Seidel-Walsh theorem together with some subsequent results. 相似文献
16.
In 1921, Blichfeldt gave an upper bound on the number of integral points contained in a convex body in terms of the volume
of the body. More precisely, he showed that
#(K?\Bbb Zn) £ n! vol(K)+n\#(K\cap{\Bbb Z}^n)\le n! {\rm vol}(K)+n
, whenever
K ì \Bbb RnK\subset{\Bbb R}^n
is a convex body containing n + 1 affinely independent integral points. Here we prove an analogous inequality with respect to the surface area F(K), namely
#(K?\Bbb Zn) < vol(K) + ((?n+1)/2) (n-1)! F(K)\#(K\cap{\Bbb Z}^n) < {\rm vol}(K) + ((\sqrt{n}+1)/2) (n-1)! {\rm F}(K)
. The proof is based on a slight improvement of Blichfeldt’s bound in the case when K is a non-lattice translate of a lattice polytope, i.e., K = t + P, where
t ? \Bbb Rn\\Bbb Znt\in{\Bbb R}^n\setminus{\Bbb Z}^n
and P is an n-dimensional polytope with integral vertices. Then we have
#((t+P)?\Bbb Zn) £ n! vol(P)\#((t+P)\cap{\Bbb Z}^n)\le n! {\rm vol}(P)
.
Moreover, in the 3-dimensional case we prove a stronger inequality, namely
#(K?\Bbb Zn) < vol(K) + 2 F(K)\#(K\cap{\Bbb Z}^n)< {\rm vol}(K) + 2 {\rm F}(K)
. 相似文献
17.
Emmanuel Preissmann 《Monatshefte für Mathematik》2007,45(1):233-239
Let X
0 be the germ at 0 of a complex variety and let
f: X0? \Bbb Cn0f:\ X_0\rightarrow {\Bbb C}^n_0
be a holomorphic germ. We say that f is pseudoimmersive if for any
g: \Bbb R0? X0g:\ {\Bbb R}_0\rightarrow X_0
such that
f °g ? C¥ f \circ g \in C^{\infty}
, we have
g ? C¥g\in C^{\infty}
. We prove that f is pseudoimmersive if and only if it is injective. Some results about the real case are also considered. 相似文献
18.
Zhiting Xu 《Monatshefte für Mathematik》2007,57(5):157-171
Some oscillation criteria are established by the averaging technique for the second order neutral delay differential equation
of Emden-Fowler type
(a(t)x¢(t))¢+q1(t)| y(t-s1)|a sgn y(t-s1) +q2(t)| y(t-s2)|b sgn y(t-s2)=0, t 3 t0,(a(t)x'(t))'+q_1(t)| y(t-\sigma_1)|^{\alpha}\,{\rm sgn}\,y(t-\sigma_1) +q_2(t)| y(t-\sigma_2)|^{\beta}\,{\rm sgn}\,y(t-\sigma_2)=0,\quad t \ge t_0,
where x(t) = y(t) + p(t)y(t − τ), τ, σ1 and σ2 are nonnegative constants, α > 0, β > 0, and a, p, q
1,
q2 ? C([t0, ¥), \Bbb R)q_2\in C([t_0, \infty), {\Bbb R})
. The results of this paper extend and improve some known results. In particular, two interesting examples that point out
the importance of our theorems are also included. 相似文献
19.
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
20.
Given two sets
A, B í \Bbb Fqd{\cal A}, {\cal B}\subseteq {\Bbb F}_q^d
, the set of d dimensional vectors over the finite field
\Bbb Fq{\Bbb F}_q
with q elements, we show that the sumset
A+B = {a+b | a ? A, b ? B}{\cal A}+{\cal B} = \{{\bf a}+{\bf b}\ \vert\ {\bf a} \in {\cal A}, {\bf b} \in {\cal B}\}
contains a geometric progression of length k of the form vΛ
j
, where j = 0,…, k − 1, with a nonzero vector
v ? \Bbb Fqd{\bf v} \in {\Bbb F}_q^d
and a nonsingular d × d matrix Λ whenever
# A # B 3 20 q2d-2/k\# {\cal A} \# {\cal B} \ge 20 q^{2d-2/k}
. We also consider some modifications of this problem including the question of the existence of elements of sumsets on algebraic
varieties. 相似文献