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1.
We consider a complex symmetric sequence space E that possesses the Fatou property and is different from l2. We prove that, for every surjective linear isometry V on E, there exist λ n ∈ ? with |λ n | = 1 and a bijective mapping π on the set ? of natural numbers such that for every {ξ n {n∈? ∈ E.
相似文献
$$V\left( {\left\{ {\xi _n } \right\}_{n \in \mathbb{N}} } \right) = \left\{ {\lambda _n \xi _{\pi (n)} } \right\}_{n \in \mathbb{N}}$$
2.
Genkai Zhang 《Israel Journal of Mathematics》2000,119(1):157-185
Let
be the invariant Cauchy Riemann operator and
the corresponding invariant Laplacians on a bounded symmetric domain. We calculate the eigenvalues ofM
m
on spherical functions. In particular we prove that for a symmetric domain of rank two the operatorsM
1,M
3 generate all invariant differential operators. We also find the eigenvalues of the generators introduced by Shimura. 相似文献
3.
4.
《复变函数与椭圆型方程》2012,57(10):865-876
We prove a Fatou-type theorem on a homogeneous line bundle over a Hermitian symmetric space, and characterize the range of the Poisson transform of Lp -functions on the maximal boundary as a Hardy-type space. 相似文献
5.
Antonio J. Di Scala 《Advances in Mathematics》2008,217(5):2336-2352
Let M⊂Cn be a complex n-dimensional Hermitian symmetric space endowed with the hyperbolic form ωhyp. Denote by (M∗,ωFS) the compact dual of (M,ωhyp), where ωFS is the Fubini-Study form on M∗. Our first result is Theorem 1.1 where, with the aid of the theory of Jordan triple systems, we construct an explicit symplectic duality, namely a diffeomorphism satisfying and for the pull-back of ΨM, where ω0 is the restriction to M of the flat Kähler form of the Hermitian positive Jordan triple system associated to M. Amongst other properties of the map ΨM, we also show that it takes (complete) complex and totally geodesic submanifolds of M through the origin to complex linear subspaces of Cn. As a byproduct of the proof of Theorem 1.1 we get an interesting characterization (Theorem 5.3) of the Bergman form of a Hermitian symmetric space in terms of its restriction to classical complex and totally geodesic submanifolds passing through the origin. 相似文献
6.
On an almost Hermitian manifold (M, g, J) one considers the naturally defined field of local diffeomorphismsj
m
=exp
m
J
m
exp
m
–1
,mM, and in particular, one studies isometric, harmonic, holomorphic and symplecticj
m
. This leads to some characterizations of special classes of almost Hermitian manifolds, including the class of Hermitian symmetric spaces. In addition, one treats some intrinsic and extrinsic geometrical properties of geodesic spheres relating to these local diffeomorphisms.Supported by grant 203.01.50 of the C.N.R., Italy. 相似文献
7.
We characterize irreducible Hermitian symmetric spaces which are not of tube type, both in terms of
the topology of the space of triples of pairwise transverse points in the Shilov boundary, and of two invariants which we
introduce, the Hermitian triple product and its complexification. We apply these results and the techniques introduced in
[6] to characterize conjugacy classes of Zariski dense representations of a locally compact group into the connected component
G of the isometry group of an irreducible Hermitian symmetric space which is not of tube type, in terms of the pullback of
the bounded Kahler class via the representation. We conclude also that if the second bounded cohomology of a finitely generated
group Γ is finite dimensional, then there are only finitely many conjugacy classes of representations of Γ into G with Zariski
dense image. This generalizes results of [6]. 相似文献
8.
Amassa Fauntleroy 《Mathematical Intelligencer》1993,15(2):27-32
This paper is a written version of the NAM William Claytor Lecture delivered at the 1991 Annual Meeting of the AMS-MAA-NAM,
January 1991 in San Frandsco, CA. 相似文献
9.
L. Clozel 《Proceedings Mathematical Sciences》2007,117(3):317-323
We prove that equivariant, holomorphic embeddings of Hermitian symmetric spaces are totally geodesic (when the image is not
of exceptional type). 相似文献
10.
Genkai Zhang 《manuscripta mathematica》1998,97(3):371-388
Let X=G
* be a compact Hermitian symmetric space. We study the Berezin transform on L
2(X) and calculate its spectrum under the decomposition of L
2(X) into the irreducible representations of G
*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical
line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X.
Received: 10 September 1996 / Revised version: 10 September 1997 相似文献
11.
12.
Andrea Loi 《Differential Geometry and its Applications》2006,24(3):311-319
In this paper we study the Calabi diastasis function of Hermitian symmetric spaces. This allows us to prove that if a complete Hermitian locally symmetric space (M,g) admits a Kähler immersion into a globally symmetric space (S,G) then it is globally symmetric and the immersion is injective. Moreover, if (S,G) is symmetric of a specified type (Euclidean, noncompact, compact), then (M,g) is of the same type. We also give a characterization of Hermitian globally symmetric spaces in terms of their diastasis function. Finally, we apply our analysis to study the balanced metrics, introduced by Donaldson, in the case of locally Hermitian symmetric spaces. 相似文献
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15.
16.
In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schrodinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the nonautonomous (inhomogeneous) Schrodinger flow from S1 into a Hermitian locally symmetric space admits a unique global smooth solution, and then we address the global existence of the Cauchy problem of inhomogeneous Heisenberg spin ferromagnet system. 相似文献
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18.
19.
We show that the secant varieties of rank three compact Hermitian symmetric spaces in their minimal homogeneous embeddings are normal, with rational singularities. We show that their ideals are generated in degree three—with one exception, the secant variety of the 21-dimensional spinor variety in P63 where we show that the ideal is generated in degree four. We also discuss the coordinate rings of secant varieties of compact Hermitian symmetric spaces. 相似文献