共查询到20条相似文献,搜索用时 421 毫秒
1.
Piernicola Bettiol 《Journal of Mathematical Sciences》2007,144(1):3760-3774
Consider an initial Lagrangian submanifold Λ0 ⊂ T* ℝ
n
that admits a global generating function and a Hamiltonian isotopy Φ
H
t
. Then, we provide a global generating function for the Lagrangian submanifold Λ
t
= Φ
H
t
(Λ0) realized by applying the so-called Amann-Conley-Zehnder reduction. When Λ0 is the zero-section, we study in some detail the asymptotic behavior of such generating functions and give an approximation
result.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal
Conference-2004, Part 1, 2005. 相似文献
2.
R. Ya. Nizkii 《Journal of Mathematical Sciences》2007,140(4):564-581
Let M0 be the Minkowski space, let Λ2(M0) be the space of bivectors in M0, and let G1 ⊂ Λ2(M0) be the manifold of directions of the physical space, consisting of simple bivectors with square −1. A mapping F: U → Λ2(M0), U ⊂ ℝ4, satisfying the Maxwell equations is regarded as the tensor of an electromagnetic field in vacuum. The field is described
on the basis of a special decomposition F = eω + h(*ω), where the mapping ω: U → G1 is called the direction of the field, and e: U → (0, +∞) and h: U → ℝ are the electric and magnetic coefficients of the field.
The Maxwell equations are reformulated in terms of ω, e, and h. Electromagnetic fields whose set of directions is a point
or a one-dimensional subset of G1 are considered. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 118–146. 相似文献
3.
A. I. Pavlov 《Mathematical Notes》1997,62(6):739-746
Let Λ be an arbitrary set of positive integers andS
n
(Λ) the set of all permutations of degreen for which the lengths of all cycles belong to the set Λ. In the paper the asymptotics of the ratio |S
n
(Λ)|/n! asn→∞ is studied in the following cases: 1) Λ is the union of finitely many arithmetic progressions, 2) Λ consists of all positive
integers that are not divisible by any number from a given finite set of pairwise coprime positive integers. Here |S
n
(Λ)| stands for the number of elements in the finite setS
n
(Λ).
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 881–891, December, 1997.
Translated by A. I. Shtern 相似文献
4.
Deguang Han 《Journal of Fourier Analysis and Applications》2009,15(2):201-217
Let
be a full rank time-frequency lattice in ℝ
d
×ℝ
d
. In this note we first prove that any dual Gabor frame pair for a Λ-shift invariant subspace M can be dilated to a dual Gabor frame pair for the whole space L
2(ℝ
d
) when the volume v(Λ) of the lattice Λ satisfies the condition v(Λ)≤1, and to a dual Gabor Riesz basis pair for a Λ-shift
invariant subspace containing M when v(Λ)>1. This generalizes the dilation result in Gabardo and Han (J. Fourier Anal. Appl. 7:419–433, [2001]) to both higher dimensions and dual subspace Gabor frame pairs. Secondly, for any fixed positive integer N, we investigate the problem whether any Bessel–Gabor family G(g,Λ) can be completed to a tight Gabor (multi-)frame G(g,Λ)∪(∪
j=1
N
G(g
j
,Λ)) for L
2(ℝ
d
). We show that this is true whenever v(Λ)≤N. In particular, when v(Λ)≤1, any Bessel–Gabor system is a subset of a tight Gabor frame G(g,Λ)∪G(h,Λ) for L
2(ℝ
d
). Related results for affine systems are also discussed.
Communicated by Chris Heil. 相似文献
5.
V. Maiorov 《Advances in Computational Mathematics》2006,25(4):435-450
We consider the manifolds H
n(φ) formed by all possible linear combinations of n functions from the set {φ(A⋅+b)}, where x→Ax+b is arbitrary affine mapping in the space ℝd. For example, neural networks and radial basis functions are the manifolds of type H
n(φ). We obtain estimates for pseudo-dimension of the manifold H
n(φ) for wide collection of the generator function φ. The estimates have the order O(d
2
n) in degree scale, that is the order is proportional to number of parameters of the manifold H
n(φ). Moreover the estimates for ɛ-entropy of the manifold H
n(φ) are obtained.
Mathematics subject classifications (2000) 41A46, 41A50, 42A61, 42C10
V. Maiorov: Supported by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel. 相似文献
6.
Antonio J. Di Scala 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2009,79(1):37-46
Let M⊂ℝ
n
be a submanifold of a euclidean space. A vector d∈ℝ
n
is called a helix direction of M if the angle between d and any tangent space T
p
M is constant. Let ℋ(M) be the set of helix directions of M. If the set ℋ(M) contains r linearly independent vectors we say that M is a weak r-helix. We say that M is a strong r-helix if ℋ(M) is a r-dimensional linear subspace of ℝ
n
. For curves and hypersurfaces both definitions agree. The object of this article is to show that these definitions are not
equivalent. Namely, we construct (non strong) weak 2-helix surfaces of ℝ4.
The author is supported by the Project M.I.U.R. “Riemann Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.,
Italy. 相似文献
7.
A. B. Aleksandrov 《Journal of Mathematical Sciences》2008,148(6):785-794
We prove that each translation and dilation invariant subspace X ⊂ L
p
(ℝn), X ≠ L
p
(ℝn), is contained in a maximal translation and dilation invariant subspace of L
p
(ℝn). Moreover, we prove that the set of all maximal translation and dilation invariant subspaces of L
p
(ℝn) has the power of continuum. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 5–21. 相似文献
8.
Jianwei Zhou 《Acta Mathematica Hungarica》2006,111(1-2):29-41
Summary We study minimal and totally geodesic submanifolds in Lie groups and related problems. We show that: (1) The imbedding of
the Grassmann manifold GF(n,N) in the Lie group GF(N) defined naturally makes GF(n,N) a totally geodesic submanifold; (2) The imbedding S7→SO(8) defined by octonians makes S7a totally geodesic submanifold inSO(8); (3) The natural inclusion of the Lie group GF(N) in the sphere ScN^2-1(√N) of gl(N,F)is minimal. Therefore the natural imbedding GF(N)<span style='font-size:10.0pt;font-family:"Lucida Sans Unicode"'>→gl(N,F)is formed by the eigenfunctions of the Laplacian on GF(N). 相似文献
9.
Hai-Ping Fu 《Proceedings Mathematical Sciences》2010,120(4):457-464
Let M
n
(n ≥ 3) be an n-dimensional complete immersed $
\frac{{n - 2}}
{n}
$
\frac{{n - 2}}
{n}
-super-stable minimal submanifold in an (n + p)-dimensional Euclidean space ℝ
n+p
with flat normal bundle. We prove that if the second fundamental form of M satisfies some decay conditions, then M is an affine plane or a catenoid in some Euclidean subspace. 相似文献
10.
We characterize the discrete sets Λ⊆ℝ such that {φ(t−λ),λ∈Λ} span L
1(ℝ), φ being an L
1(ℝ)-function whose Fourier transform behaves like e
−2π|ξ|. 相似文献
11.
Liguang Liu 《Frontiers of Mathematics in China》2007,2(4):599-611
Let ℐ(ℝn) be the Schwartz class on ℝn and ℐ∞(ℝn) be the collection of functions ϕ ∊ ℐ(ℝn) with additional property that
for all multiindices γ. Let (ℐ(ℝn))′ and (ℐ∞(ℝn))′ be their dual spaces, respectively. In this paper, it is proved that atomic Hardy spaces defined via (ℐ(ℝn))′ and (ℐ∞(ℝn))′ coincide with each other in some sense. As an application, we show that under the condition that the Littlewood-Paley
function of f belongs to L
p(ℝn) for some p ∊ (0,1], the condition f ∊ (ℐ∞(ℝn))′ is equivalent to that f ∊ (ℐ(ℝn))′ and f vanishes weakly at infinity. We further discuss some new classes of distributions defined via ℐ(ℝn) and ℐ∞(ℝn), also including their corresponding Hardy spaces.
相似文献
12.
A. V. Potepun 《Journal of Mathematical Sciences》2007,141(5):1545-1556
In part I of the paper, we have defined n-dimensional C0-manifolds in ℝn(m ≥ n) with locally-finite n-dimensional variations (a generalization of locally-rectifiable curves to dimensionn > 1) and
integration of measurable differential n-forms over such manifolds. The main result of part II states that an n-dimensional
manifold that is C1-embedded into ℝm has locally-finite variations and the integral of a measurable differential n-form defined in part I can be calculated by
the well-known formula. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 66–85. 相似文献
13.
Given two Banach spaces E,F, let B(E,F) be the set of all bounded linear operators from E into F, Σ
r
the set of all operators of finite rank r in B(E,F), and Σ
r
# the number of path connected components of Σ
r
. It is known that Σ
r
is a smooth Banach submanifold in B(E,F) with given expression of its tangent space at each A ∈ Σ
r
. In this paper,the equality Σ
r
# = 1 is proved. Consequently, the following theorem is obtained: for any nonnegative integer r, Σ
r
is a smooth and path connected Banach submanifold in B(E,F) with the tangent space T
A
Σ
r
= {B ∈ B(E,F): BN(A) ⊂ R(A)} at each A ∈ Σ
r
if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property
of Σ
r
the method presented in this paper is also interesting. As an application of this result, it is proved that if E = ℝ
n
and F = ℝ
m
, then Σ
r
is a smooth and path connected submanifold of B(ℝ
n
, ℝ
m
) and its dimension is dimΣ
r
= (m+n)r−r
2 for each r, 0 <- r < min {n,m}.
Supported by the National Science Foundation of China (Grant No.10671049 and 10771101). 相似文献
14.
E. L. Alexandrov 《Mathematical Notes》2000,67(6):679-685
Explicit formulas are derived for the spectral function of double multiplication operator containing a multiplicative evolution
inL
2(X, μ)-space and a convolution-type operator inL
2(ℝ
n
)-spaces. Symmetric convolution and multiplication operators are considered inL
2(X, μ) andL
2(ℝ
n
)-spaces.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 803–810, June, 2000. 相似文献
15.
M. Yu. Nikanorova 《Journal of Mathematical Sciences》2007,140(4):582-588
The structure of the tangent bundle of the real Grassmann manifold G
+
p,n
under the Plücker embedding (in the exterior algebra of the initial Euclidean space) is studied. Explicit expressions for
the relation between decompositions of a tangent vector with respect to different bases of the tangent space are obtained,
and a constructivemethod yielding the canonical (= simplest) decomposition is presented. Bibliography: 8 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 147–158. 相似文献
16.
R. A. Dwyer 《Discrete and Computational Geometry》1997,17(2):123-136
It is proved that, for any fixedd ≽ 3 and 0 ≤k ≤ d - 1, the expected combinatorial complexity of the Euclidean Voronoi diagram ofn random &-flats drawn independently from the uniform distribution onk-flats intersecting the unit ball in ℝd is Ξ(n
d/(d-k)) asn → ∞. A by-product of the proof is a density transformation for integrating over sets ofd + 1k-flats in ℝd 相似文献
17.
A subgroup D of GL (n, ℝ) is said to be admissible if the semidirect product of D and ℝ
n
, considered as a subgroup of the affine group on ℝ
n
, admits wavelets ψ ∈ L2(ℝ
n
) satisfying a generalization of the Calderón reproducing, formula. This article provides a nearly complete characterization
of the admissible subgroups D. More precisely, if D is admissible, then the stability subgroup Dx for the transpose action of D on ℝ
n
must be compact for a. e. x. ∈ ℝ
n
; moreover, if Δ is the modular function of D, there must exist an a ∈ D such that |det a| ≠ Δ(a). Conversely, if the last condition holds and for a. e. x ∈ ℝ
n
there exists an ε > 0 for which the ε-stabilizer D
x
ε
is compact, then D is admissible. Numerous examples are given of both admissible and non-admissible groups. 相似文献
18.
In this paper we establish a discrete Calderón’s identity which converges in both L
q
(ℝ
n+m
) (1<q<∞) and Hardy space H
p
(ℝ
n
×ℝ
m
) (0<p≤1). Based on this identity, we derive a new atomic decomposition into (p,q)-atoms (1<q<∞) on H
p
(ℝ
n
×ℝ
m
) for 0<p≤1. As an application, we prove that an operator T, which is bounded on L
q
(ℝ
n+m
) for some 1<q<∞, is bounded from H
p
(ℝ
n
×ℝ
m
) to L
p
(ℝ
n+m
) if and only if T is bounded uniformly on all (p,q)-product atoms in L
p
(ℝ
n+m
). The similar result from H
p
(ℝ
n
×ℝ
m
) to H
p
(ℝ
n
×ℝ
m
) is also obtained. 相似文献
19.
Incompleteness and minimality of complex exponential system 总被引:3,自引:0,他引:3
Guan-tie DENG School of Mathematical Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2007,50(10):1467-1476
A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A,M)in C_α,where C_αis the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t))vanishing at infinity,in the uniform norm‖f‖_α=sup{|f(t)e~(-α(t))|:t∈R}with respect to the weightα(t).If the incompleteness holds, then the complex exponential system E(?)is minimal and each function in the closure of the linear span of complex exponential system E(?)can be extended to an entire function represented by a Taylor-Dirichlet series. 相似文献
20.
Robert S. Strichartz 《Journal d'Analyse Mathématique》2006,99(1):333-353
For certain Cantor measures μ on ℝn, it was shown by Jorgensen and Pedersen that there exists an orthonormal basis of exponentialse
2πiγ·x for λεΛ. a discrete subset of ℝn called aspectrum for μ. For anyL
1 functionf, we define coefficientsc
γ(f)=∝f(y)e
−2πiγiy
dμ(y) and form the Mock Fourier series ∑λ∈Λcλ(f)e
2πiλ·x
. There is a natural sequence of finite subsets Λn increasing to Λ asn→∞, and we define the partial sums of the Mock Fourier series by
We prove, under mild technical assumptions on μ and Λ, thats
n(f) converges uniformly tof for any continuous functionf and obtain the rate of convergence in terms of the modulus of continuity off. We also show, under somewhat stronger hypotheses, almost everywhere convergence forfεL
1.
Research supported in part by the National Science Foundation, Grant DMS-0140194. 相似文献