논문KCI 등재
FOURIER TRANSFORM AND Lp-MIXED PROJECTION BODIES
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper we define the Lp-mixed curvature function of a convex body. We develop a formula connection the support function of Lp-mixed projection body with Fourier transform of the Lp-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for Lp-mixed projection bodies.
Abstract
In this paper we define the Lp-mixed curvature function of a convex body. We develop a formula connection the support function of Lp-mixed projection body with Fourier transform of the Lp-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for Lp-mixed projection bodies.
참고문헌 (17)
- R. J. Gardner, "Geometric Tomography, Second edition. Encyclopedia of Mathematics and its Applications, 58" (2006), Cambridge University Press
- R. J. Gardner, "An analytic solution to the Busemann-Petty problem on sections of convex bodies", Ann. of Math., 149(2), pp.691~703 (1999)
- I. M. Gelfand, "Generalized Functions. Vol. 1, Properties and operations" (1964), Academic Press
- I. M. Gelfand, "Generalized Functions" (1964), Academic Press
- A. Koldobsky, "Intersection bodies, positive definite distributions, and the Busemann-Petty problem", Amer. J. Math., 120(4), pp.827~840 (1998)
- A. Koldobsky, "A generalization of the Busemann-Petty problem on sections of convex bodies", Israel J. Math., 110, pp.75~91 (1999)
- A. Koldobsky, "Fourier Analysis in Convex Geometry" (2005), American Mathematical Society
- A. Koldobsky, "Projections of convex bodies and the Fourier transform", Israel J. Math., 139, pp.361~380 (2004)
- E. Lutwak, "The Brunn-Minkowski-Firey theory. Ⅰ. Mixed volumes and the Minkowski problem", J. Differential Geom., 38(1), pp.131~150 (1993)
- E. Lutwak, "The Brunn-Minkowski-Firey theory. Ⅱ. Affine and geominimal surface areas", Adv. Math., 118(2), pp.244~294 (1996)
- E. Lutwak, "Lp affine isoperimetric inequalities", J. Differential Geom., 56(1), pp.111~132 (2000)
- S. J. Lv, "On an analytic generalization of the Busemann-Petty problem", J. Math. Anal. Appl., 341(2), pp.1438~1444 (2008)
- C. M. Petty, "Projection bodies", Proc. Colloquium on Convexity, pp.234~241 (1967), Kobenhavns Univ. Mat. Inst.
- D. Ryabogin, "The Fourier transform and Firey projections of convex bodies", Indiana Univ. Math. J., 53(3), pp.667~682 (2004)
- R. Schneider, "Zur einem Problem von Shephard uber die Projektionen konvexer Körper", Math. Z., 101, pp.71~82 (1967)
- R. Schneider, "Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, 44" (1993), Cambridge University Press
- A. Zvavitch, "The Busemann-Petty problem for arbitrary measures", Math. Ann., 331(4), pp.867~887 (2005)
관련 논문AI추천
VOLUME INEQUALITIES FOR THE L p-SINE TRANSFORM OF ISOTROPIC MEASURESGangsong Leng, LuJun Guo대한수학회 · 대한수학회보2015 · 제52권 제3호ON POLARS OF MIXED COMPLEX PROJECTION BODIESLijuan Liu, Qingzhong Huang, Wei Wang대한수학회 · 대한수학회보2015 · 제52권 제2호A stability result for p-centroid bodiesGangsong Leng, LuJun Guo, Youjiang Lin대한수학회 · 대한수학회보2018 · 제55권 제1호Inequalities for Chord power integralsGe Xiong, Xiaogang Song대한수학회 · 대한수학회지2008 · 제45권 제2호MIXED CHORD-INTEGRALS OF STAR BODIESDepartment of Mathematics대한수학회 · 대한수학회지2010 · 제47권 제2호EXTREMUM PROPERTIES OF DUAL Lp-CENTROID BODY AND Lp-JOHN ELLIPSOIDTong-Yi Ma대한수학회 · 대한수학회보2012 · 제49권 제3호
이 간행물의 다른 논문 (17건)
ON ARMENDARIZ IDEALSSh. Ghalandarzadeh, H. Haj Seyyed Javadi, M. Shamsaddini Fard, M. Khoramdelpp. 883-888CONSISTENT AND ASYMPTOTICALLY NORMAL ESTIMATORS FOR PERIODIC BILINEAR MODELSAntony Gautier, Abdelouahab Bibipp. 889-905THE KRONECKER FUNCTION RING OF THE RING D[X]N장규환pp. 907-913EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY한상언pp. 915-932SETS OF UNIQUENESS, WEAKLY SUFFICIENT SETS AND SAMPLING SETS FOR A-∞(B)Le Hai Khoipp. 933-950