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1.
Loren D. Pitt 《Israel Journal of Mathematics》1976,24(2):94-118
For a fixed weight Δ(dx) onR
1 and a linear space ℋ ⊆L
p(Δ) of entire functions that is closed under difference quotientsh(·)→(z−·)
−1[h(z)−h(·)], theL
p(Δ) closure
of ℋ is studied and characterized in terms of the normsL(z), (z∈C
1 of the evaluation functionalsh→h(z),h∈ℋ.
Partially supported by DA-ARO-31-124-71-6182 and NSF GP-43011. 相似文献
2.
Yongge Tian 《Advances in Applied Clifford Algebras》2000,10(1):61-90
As is well-known, the real quaternion division algebra ℍ is algebraically isomorphic to a 4-by-4 real matrix algebra. But
the real division octonion algebra
can not be algebraically isomorphic to any matrix algebras over the real number field ℝ, because
is a non-associative algebra over ℝ. However since
is an extension of ℍ by the Cayley-Dickson process and is also finite-dimensional, some pseudo real matrix representations
of octonions can still be introduced through real matrix representations of quaternions. In this paper we give a complete
investigation to real matrix representations of octonions, and consider their various applications to octonions as well as
matrices of octonions. 相似文献
3.
Gil Kalai 《Israel Journal of Mathematics》1983,45(4):337-351
Let
(n, k) be the class of all simplicial complexesC over a fixed set ofn vertices (2≦k≦n) such that: (1)C has a complete (k−1)-skeleton, (2)C has precisely (
k
n−1
)k-faces, (3)H
k
(C)=0. We prove that for
,H
k−1(C) is a finite group, and our main result is:
. This formula extends to high dimensions Cayley’s formula for the number of trees onn labelled vertices. Its proof is based on a generalization of the matrix tree theorem. 相似文献
4.
In this paper we consider operators acting on a subspace ℳ of the space L
2 (ℝm; ℂm) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace
ℳ is defined as the orthogonal sum of spaces ℳs,k of specific Clifford basis functions of L
2(ℝm; ℂm).
Every Clifford endomorphism of ℳ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic
operators are characterized in terms of commutation relations and they transform a space ℳs,k into a similar space ℳs′,k′. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ℳ is known.
Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is
studied in detail. 相似文献
5.
Geoffrey S. Watson 《Annals of the Institute of Statistical Mathematics》1983,35(1):303-319
Summary A distribution on the unit sphere inℝ
q
with a densityf(‖x
v
‖) is considered where
is ans(<q) dimensional subspace andx
v
is the part ofx in
. For a large sample the estimation of
, a test that
and a test for rotational symmetry within
is given. For several samples with possibly different subspaces
but the samef, a test that
is given. For all tests power functions for contiguous alternatives are given. For the special density proportional to expk‖x
v
‖
2, additional results are given.
Research supported in part by a Contract with the Office of Naval Research N00014-81-K-0146 awarded to Princeton University,
Princeton, New Jersey 08544. 相似文献
6.
The Marcinkiewicz-Zygmund inequality and the Bernstein inequality are established on ∮2m(T,R)∩L2(R) which is the space of polynomial splines with irregularly distributed nodes T={tj}j∈Z, where {tj}j∈Z is a real sequence such that {eitξ}j∈Z constitutes a Riesz basis for L2([-π,π]). From these results, the asymptotic relation E(f,Bπ,2)2=lim E(f,∮2m(T,R)∩L2(R))2 is proved, where Bπ,2 denotes the set of all functions from L2(R) which can be continued to entire functions of exponential type ≤π, i.e. the classical Paley-Wiener class. 相似文献
7.
Sigmundur Gudmundsson 《manuscripta mathematica》1997,93(1):421-433
Summary In this paper we give a unified framework for constructing harmonic morphisms from the irreducible Riemannian symmetric spaces
ℍH
n, ℂH
n, ℝH
2
t+1, ℍP
n, ℂP
n and ℝP
2n+1 of rank one. Using this we give a positive answer to the global existence problem for the non-compact hyperbolic cases.
This work was supported by The Swedish Natural Science Research Council.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
8.
HE Yijun & WANG Changping LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(3):341-349
Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(?) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(?)RPn(?) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (?) RPn(?) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space. 相似文献
9.
This note proves that, forF = ℝ, ℂ or ℍ, the bordism classes of all non-bounding Grassmannian manifoldsG
k(F
n+k), withk <n and having real dimensiond, constitute a linearly independent set in the unoriented bordism group N
d
regarded as a ℤ2-vector space. 相似文献
10.
We show that if a closed manifold M admits an ℱ-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular,
this is the case if M admits a non-trivial S
1-action. As a corollary we obtain that the simplicial volume of a manifold admitting an ℱ-structure is zero.?We also show
that if M admits an ℱ-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently, its Yamabe invariant is non-negative.?We show that ℱ-structures
of rank zero appear rather frequently: every compact complex elliptic surface admits one as well as any simply connected closed
5-manifold.?We use these results to study the minimal entropy problem. We show the following two theorems: suppose that M is a closed manifold obtained by taking connected sums of copies of S
4, ℂP
2,
2,S
2×S
2and the K3 surface. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
4,ℂP
2,S
2×S
2,ℂP
2#
2 or ℂP
2# ℂP
2. Finally, suppose that M is a closed simply connected 5-manifold. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
5,S
3×S
2, then on trivial S
3-bundle over S
2 or the Wu-manifold SU(3)/SO(3).
Oblatum 13-III-2002 & 12-VIII-2002?Published online: 8 November 2002
G.P. Paternain was partially supported by CIMAT, Guanajuato, México.?J. Petean is supported by grant 37558-E of CONACYT. 相似文献
11.
J. A. S. Martins 《Annali di Matematica Pura ed Applicata》1977,115(1):271-294
Summary Piecewise polynomial and Fourier approximation of functions in the Sobolev spaces
on unbounded domains Θ ⊂ Rn are applied to the study of the type of compact embeddings into appropriate Lebesgue and Orlicz spaces. It is shown that
if Θ and s satisfy certain conditions, the embeddings
, m/n+1/q−1/p>0 and
, Φ being an Orlicz function subordinate to both φ(t)=|t|p
exp |t|n/(n−m) and Φσ(t)=exp |t|σ−1, σ ⩾ 1, m/n>1/p, are of type ls. One result dealing with multiplications maps from
into Lq(Θ) is also obtained.
Entrata in Redazione il 14 ottobre 1976. 相似文献
12.
We provide conditions on the complex dilatation of a homeomorphismf of the upper half plane ℍ into ℂ, which guarantee thatf(ℍ) is a proper subset of ℂ and, in case wheref(ℍ) is a Jordan domain, thatf has a homeomorphic extension onto
. 相似文献
13.
Shmuel Kantorovitz 《Semigroup Forum》2009,78(2):285-292
The “Volterra relation” is the commutation relation [S,V]⊂V
2, where S is a not necessarily bounded operator, V is a bounded operator leaving D(S) invariant, and [⋅,⋅] is the Lie product. When S,V are so related, and in addition iS generates a bounded C
0-group of operators and V has some general property, it is known that S+α
V (α∈ℂ) is similar to S if and only if ℜ
α=0 (cf. Theorem 11.17 in Kantorovitz, Spectral Theory of Banach Space Operators, Springer, Berlin, 1983). In particular, S−V is not similar to S. However, it is shown in this note that (without any restriction on
V
and on the group
S(⋅) generated by
iS), the perturbations (S−V)+P are similar to S for all P in the similarity sub-orbit {S(a)VS(−a);a∈ℝ} of V. When S is bounded, the above perturbations are similar to S for all P in the wider similarity sub-orbit {e
aS
Ve
−aS
;a∈ℂ}. 相似文献
14.
Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for any continuous mapf: Gn,k → Gn,k, dim Gn,k = dim Gm,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂGm,l → ℂGn,k,h: ℍGm,l → ℍGn,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained. 相似文献
15.
This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category:
and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of
and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give
a sufficient and necessary condition for the braid of,
Hℳ to induce the braid of
, or equivalently, the braid of
, whereA is a quantum commutativeH-module algebra 相似文献
16.
Harish Seshadri 《Proceedings Mathematical Sciences》2009,119(2):197-201
Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension ≥ 3. Suppose that the sectional curvature K satisfies −1 − s(r) ≤ K ≤ −1, where r denotes distance to a fixed point in M. If lim
r → ∞ e2r
s(r) = 0, then (M, g) has to be isometric to ℍ
n
.
The same proof also yields that if K satisfies −s(r) ≤ K ≤ 0 where lim
r → ∞
r
2
s(r) = 0, then (M, g) is isometric to ℝ
n
, a result due to Greene and Wu.
Our second result is a local one: Let (M, g) be any Riemannian manifold. For a ∈ ℝ, if K ≤ a on a geodesic ball B
p
(R) in M and K = a on ∂B
p
(R), then K = a on B
p
(R). 相似文献
17.
Ch. G. Philos 《Annali di Matematica Pura ed Applicata》1979,119(1):25-40
Summary This paper is dealing with the oscillatory and asymptotic behavior of the bounded solutions of n-th order (n>1) differential equations with deviating arguments involving the so called r-derivatives D
r
(i)x
(i=0, 1, ..., n) of the unknown function x defined by
, where ri (i=1, 2, ..., n−1) are positive continuous functions on the interval [t
0
, ∞). The fundamental purpose is to find a necessary and sufficient condition in order to have at least one (bounded nonoscillatory)
solution whose the limit at ∞ exists inR−{0}.
Entrata in Redazione il 29 giugno 1977.
This paper is a part of the author's Doctoral Thesis submitted to the School of Physics and Mathematics of the University
of Ioannina. 相似文献
18.
Let G be a discrete subgroup of PU(1,n). Then G acts on ℙℂ
n
preserving the unit ball ℍℂ
n
, where it acts by isometries with respect to the Bergman metric. In this work we look at its action on all of ℙℂ
n
and determine its equicontinuity region Eq(G). This turns out to be the complement of the union of all complex projective hyperplanes in ℙℂ
n
which are tangent to ∂ℍℂ
n
at points in the Chen-Greenberg limit set Λ(G), a closed G-invariant subset of ∂ℍℂ
n
which is minimal for non-elementary groups. We also prove that the action on Eq(G) is discontinuous. Also , if the limit set is “sufficiently general” (i.e. it is not contained in any proper
k
-chain), then each connected component of Eq(G) is a holomorphy domain and it is a complete Kobayashi hyperbolic space. 相似文献
19.
Juan A. Aledo José M. Espinar José A. Gálvez 《Bulletin of the Brazilian Mathematical Society》2007,38(4):533-554
We obtain optimal height estimates for surfaces in ℍ2 × ℝ and
× ℝ with constant Gaussian curvature K(I) and positive extrinsic curvature, characterizing the extreme cases as the revolution ones. Moreover, we get a representation
for surfaces with constant Gaussian curvature in such ambient spaces, paying special attention to the cases of K(I) = 1 in
× ℝ and K(I) = −1 in ℍ2 × ℝ.
The first author is partially supported by Junta de Comunidades de Castilla-La Mancha, Grant No. PAI-05-034. The authors are
partially supported by MEC-FEDER, Grant No. MTM2007-65249. 相似文献
20.
Dionisio Gallarati 《Annali di Matematica Pura ed Applicata》1957,43(1):195-214
Sunto Si dànno delle condizioni necessarie affinchè due superficie algebriche F, G d’una V
3
algebrica non singolare possano presentare contatto d’ordine assegnato q −1 lungo una curva
priva di punti multipli. Si approfondisce sopratuito il caso q=3, con applicazione al problema di determinare le superficie algebriche Gn di S
3
che presentano contatto del 3o ordine lungo una
n con una superficie quartica F
4
. 相似文献