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81.
We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). We also give a geometric interpretation of this image in terms of valuations. In addition, we discuss the non-Archimedean analogues. 相似文献
82.
H. De Bie 《Journal of Mathematical Analysis and Applications》2008,345(1):147-164
In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the fermionic part of the Fourier kernel has a natural symplectic structure, derived using a Clifford analysis approach. Several basic properties of these three transforms are studied. Using suitable generalizations of the Hermite polynomials to superspace (see [H. De Bie, F. Sommen, Hermite and Gegenbauer polynomials in superspace using Clifford analysis, J. Phys. A 40 (2007) 10441-10456]) an eigenfunction basis for the Fourier transform is constructed. 相似文献
83.
王金平 《数学物理学报(A辑)》2006,26(1):31-038
该论文主要研究在平面情形下指数型 Radon 变换的连续性,得到了它的近似反演公式,并对近似反演的数值解法加以改进.借助一些技巧,该文从理论上还建立了精确反演公式,从而推广了古典 Radon 变换的相应结果. 相似文献
84.
On the generalized Busemann-Petty problem 总被引:1,自引:0,他引:1
The generalized Busemann-Petty problem asks whether the origin-symmetric convex bodies in ℝ
n
with a larger volume of all i-dimensional sections necessarily have a larger volume. As proved by Bourgain and Zhang, the answer to this question is negative
if i > 3. The problem is still open for i = 2, 3. In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with
a smaller i-dimensional volume belongs to given classes. Our results generalize Zhang’s specific affirmative answer to the generalized
Busemann-Petty problem.
This work was supported, in part, by the National Natural Science Foundation of China (Grant No. 10671117) 相似文献
85.
O. V. Pugachev 《Mathematical Notes》1998,63(1):94-101
We construct surface measures for surfaces of codimensionn≥1 in Banach spaces, and in a wide class of locally convex spaces. It is assumed that the determining function has a continuous
derivative along a subspace.
Translated fromMatematickeskie Zametki, Vol. 63, No. 1, pp. 106–114, January, 1998.
The author wishes to express his gratitude to V. I. Bogachev for suggesting the problem and for his valuable scientific advice. 相似文献
86.
V. I. Rybakov 《Mathematical Notes》1996,60(2):175-185
Letf be a bounded Pettis integrable function ranging in a Banach spaceX (the range of the indefinite Pettis integral is separable). We consider Pettis integrability conditions for the Stone transform off and relate this problem to the regular oscillation condition for the family of functions {x
*
fx*B(X*)}, whereB(X*) is the unit ball inX
*.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 238–253, August, 1996. 相似文献
87.
88.
89.
Shmuel Onn 《Journal of Geometry》2001,72(1-2):157-162
We provide a systematic construction of point configurations with incompatible Radon-split and Helly-core. This provides
a resolution of problems of Reay and Sierksma, and shows that it is computationally hard to decide the compatibility of the
split and core of a configuration.
Received 29 June 2000; revised 5 January 2001. 相似文献
90.
Michael Greenblatt 《Journal of Functional Analysis》2019,276(5):1510-1527
to boundedness results are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional integral kernel. In many cases, the amount of smoothing proven is optimal up to endpoints, and in such situations this amount of smoothing can be computed explicitly through the use of appropriate Newton polyhedra. 相似文献