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Paley–Wiener theorem for line bundles over compact symmetric spaces and new estimates for the Heckman–Opdam hypergeometric functions 下载免费PDF全文
《Mathematische Nachrichten》2018,291(14-15):2204-2228
Paley–Wiener type theorems describe the image of a given space of functions, often compactly supported functions, under an integral transform, usually a Fourier transform on a group or homogeneous space. In this article we proved a Paley–Wiener theorem for smooth sections f of homogeneous line bundles on a compact Riemannian symmetric space . It characterizes f with small support in terms of holomorphic extendability and exponential growth of their χ‐spherical Fourier transforms, where χ is a character of K. An important tool in our proof is a generalization of Opdam's estimate for the hypergeometric functions associated to multiplicity functions that are not necessarily positive. At the same time the radius of the domain where this estimate is valid is increased. This is done in an appendix. 相似文献
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In this paper we study mixed norm boundedness for fractional integrals related to Laplace–Beltrami operators on compact Riemannian symmetric spaces of rank one. The key point is the analysis of weighted inequalities for fractional integral operators associated to trigonometric Jacobi polynomials expansions. In particular, we find a novel sharp estimate for the Jacobi fractional integral kernel with explicit dependence on the type parameters. 相似文献
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The Fourier coefficients of a smooth K-invariant function on a compact symmetric space M=U/K are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we describe the size of the support by means of the exponential type of a holomorphic extension of the Fourier coefficients. 相似文献
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A necessary and sufficient condition is presented for a set to be a Pompeiu subset of any compact homogeneous space with a
finite invariant measure. The condition, which is expressed in terms of the intertwining operators of each primary summand
of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds. Examples are presented
demonstrating that the condition to be Pompeiu in these manifolds is quite different from the corresponding condition for
a torus of the same dimension. This provides a contrast with the existing comparison between the Heisenberg group itself and
Euclidean space in terms of Pompeiu sets. In addition, the closed linear span of all translates of any square integrable function
on any compact homogeneous space is determined. 相似文献
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《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
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Ferenc Weisz 《Integral Equations and Operator Theory》2008,60(1):133-149
So-called short-time Fourier transform multipliers (also called Anti-Wick operators in the literature) arise by applying a
pointwise multiplication operator to the STFT before applying the inverse STFT. Boundedness results are investigated for such
operators on modulation spaces and on L
p
-spaces. Because the proofs apply naturally to Wiener amalgam spaces the results are formulated in this context. Furthermore,
a version of the Hardy-Littlewood inequality for the STFT is derived.
This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship
No M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No K67642. 相似文献
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Chifune Kai 《Differential Geometry and its Applications》2005,23(1):38-54
In this paper, we show that a homogeneous tube domain is symmetric if and only if its Cayley transform image as well as the dual Cayley transform image of the dual tube domain is convex. In this case, the parameters of these Cayley transforms reduce to specific ones, so that they are essentially the usual Cayley transforms defined in terms of Jordan algebra structure. 相似文献
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M. Benyounes 《Differential Geometry and its Applications》2007,25(3):322-334
We study harmonic sections of a Riemannian vector bundle E→M when E is equipped with a 2-parameter family of metrics hp,q which includes both the Sasaki and Cheeger-Gromoll metrics. For every k>0 there exists a unique p such that the harmonic sections of the radius-k sphere subbundle are harmonic sections of E with respect to hp,q for all q. In both compact and non-compact cases, Bernstein regions of the (p,q)-plane are identified, where the only harmonic sections of E with respect to hp,q are parallel. Examples are constructed of vector fields which are harmonic sections of E=TM in the case where M is compact and has non-zero Euler characteristic. 相似文献
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We study the Jordan structures and geometry of bounded matrix-valued harmonic functions on a homogeneous space and their analogue, the harmonic functionals, in the setting of Fourier algebras of homogeneous spaces.Supported by EPSRC grant GR/G91182 and NSERC grant 7679. 相似文献
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M. Anoussis 《Advances in Mathematics》2004,188(2):425-443
Let G be a compact group, not necessarily abelian, let ? be its unitary dual, and for f∈L1(G), let fn?f∗?∗f denote n-fold convolution of f with itself and f? the Fourier transform of f. In this paper, we derive the following spectral radius formula
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In this note a representation of the discrete Green's function of a compact discretization of a two point boundary value problem of order n 2 is given which among other things allows a direct proff of the convergence (and divergence) properties. 相似文献
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P. Lefèvre 《Bulletin des Sciences Mathématiques》2004,128(9):789-801
In this paper, we are interested in a class of subspaces of C, introduced by Bourgain [Studia Math. 77 (1984) 245-253]. Wojtaszczyk called them rich in his monograph [Banach Spaces for Analysts, Cambridge Univ. Press, 1991]. We give some new examples of such spaces: this allows us to recover previous results of Godefroy-Saab and Kysliakov on spaces with reflexive annihilator in a very simple way. We construct some other examples of rich spaces, hence having property (V) of Pe?czyński and Dunford-Pettis property. We also recover the results due to Bourgain and Saccone saying that spaces of uniformly convergent Fourier series share these properties, by only using the main result of [Studia Math. 77 (1984) 245-253] and some very elementary arguments. We generalize too these results. 相似文献
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Tomoyuki Kakehi 《Advances in Mathematics》2011,(3):2739
In this paper we construct the fundamental solution to the Schödinger equation on a compact symmetric space with even root multiplicities using shift operators of Heckman and Opdam. Next, we prove that the support of the fundamental solution becomes a lower dimensional subset at a rational time whereas its support and its singular support coincide with the whole symmetric space at an irrational time. Moreover, we also show that generalized Gauss sums appear in the expression of the fundamental solution. 相似文献
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In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G. 相似文献
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Let G and H be Lie groups with Lie algebras
and
. Let G be connected. We prove that a Lie algebra homomorphism
is exact if and only if it is completely positive. The main resource is a corresponding theorem about representations on
Hilbert spaces.
This article summarizes the main results of [1].
Received: 6 December 2005 相似文献
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Summary. A univariate compactly supported refinable function can always be written as the convolution product , with the B-spline of order k,f a compactly supported distribution, and k the approximation orders provided by the underlying shift-invariant space . Factorizations of univariate refinable vectors
were also studied and utilized in the literature. One of the by-products of this article is a rigorous analysis of that factorization
notion, including, possibly, the first precise definition of that process. The main goal of this article is the introduction
of a special factorization algorithm of refinable vectors that generalizes the scalar case as closely (and unexpectedly) as
possible: the original vector is shown to be `almost' in the form , with F still compactly supported and refinable, andk the approximation order of . The algorithm guarantees F to retain the possible favorable properties of , such as the stability of the shifts of and/or the polynomiality of the mask symbol. At the same time, the theory and the algorithm are derived under relatively
mild conditions and, in particular, apply to whose shifts are not stable, as well as to refinable vectors which are not compactly supported. The usefulness of this specific
factorization for the study of the smoothness of FSI wavelets (known also as `multiwavelets' and `multiple wavelets') is explained.
The analysis invokes in an essential way the theory of finitely generated shift-invariant (FSI) spaces, and, in particular,
the tool of superfunction theory.
Received June 10, 1998 / Revised version received June 14, 1999 / Published online August 2, 2000 相似文献
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In this paper we generalize a result in [J. An, Z. Wang, On the realization of Riemannian symmetric spaces in Lie groups, Topology Appl. 153 (7) (2005) 1008-1015, showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of fixed points of involutions are also proved. 相似文献