全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

极体的体积确定凸体

, PP. 17-23

Keywords: 凸体,体积,极体

Full-Text   Cite this paper   Add to My Lib

Abstract:

利用球面调和函数和\,Hamburger\,矩方法,证明了,${\mathbb{R}}^{n}$\,中一个包含半径为\,$\delta$\,的球的原点对称凸体,能被其在此球附近的所有点的极体的体积所唯一确定.

References

[1]  {1}
[2]  MEYER M, WERNER E M. The Santal\''{o}-regions of a convex body[J].
[3]  {3}
[4]  SAINT RAYMOND J. Sur le volume des corps convexes
[5]  sym\''{e}triques[C]// S\''{e}minaire dinitiation\''{a} l''Analyse.
[6]  Paris: Univ Pierre et Marie Curie, 1980.
[7]  {6}
[8]  REISNER S. Random polytopes and the volume-product of symmetric
[9]  convex bodies[J]. Math Scand, 1985, 57: 386-392.
[10]  {7}
[11]  REISNER S. Zonoids with minimal volume-product[J]. Math Z, 1986,
[12]  2: 339-346.
[13]  {8}
[14]  REISNER S. Minimal volume product in Banach spaces with a
[15]  unconditional basis[J]. London Math Soc, 1987, 36: 126-136.
[16]  {9}
[17]  GORDON Y, MEYER M, REISNER S. Zonoids with minimal volume product-a
[18]  new proof[J]. Proc Amer Math Soc, 1988, 104: 273-276.
[19]  {10}
[20]  BOURGAIN J, MILMAN V D. New volume ratio properties for convex
[21]  symmetric bodies in Rn[J]. Invent Math, 1987, 88: 319-340.
[22]  {11}
[23]  BALL K. Mahler''s conjecture and wavelets[J]. Discrete Comput Geom,
[24]  95, 13: 271-277.
[25]  {12}
[26]  FRADELIZI M, MEYER M. Some functional forms of Blaschke-Santal\''{o}
[27]  inequality[J]. Math Z, 2007, 256: 379-395.
[28]  {18}
[29]  FRADELIZI M, MEYER M. Increasing functions and inverse Santal\''{o}
[30]  inequality for unconditional functions[J]. Positivity, 2008, 12:
[31]  Trans Amer Math Sci, 1998, 350(11): 4569-4591.
[32]  {2}
[33]  MEYER M, PAJOR A. On the Blaschke-Santal\''{o} inequality[J]. Arch
[34]  Math (Basel), 1990, 55: 82-93.
[35]  {4}
[36]  MAHLER K. Ein \"{U}bertragungsprinzip f\"{u}r Konvexe K\"{o}rper[J].
[37]  u{C}asopis P\u{e}st Mat Fys, 1939, 68: 93-102.
[38]  {5}
[39]  MAHLER K. Ein Minimalproblem f\"{u}r Konvexe Polygone[J].
[40]  Mathematica (Zutphen), 1939, 7: 118-127.
[41]  LOPEZ M A, REISNER S. A special case of Mahler''s conjecture[J].
[42]  Discrete Comput Geom, 1998, 20: 163-177.
[43]  {13}
[44]  B\"{O}R\"{O}CZKY K J, HUG D. Stability of the reverse
[45]  Blaschke-Santal\''{o} inequality for zonoids and applications[J]. Adv
[46]  Appl Math, 2010, 44: 309-328.
[47]  {14}
[48]  BARTHE F, FRADELIZI M. The volume product of convex bodies with many
[49]  {15}
[50]  ARTSTEIN S, KLARTAG B, MILMAN V D. On the Santal\''{o} point of a
[51]  function and a functional Santal\''{o} inequality[J]. Mathematika,
[52]  04, 54: 33-48.
[53]  {16}
[54]  FRADELIZI M, GORDON Y, MEYER M, et al. The case of equality for an
[55]  inverse Santal\''{o} functional inequality[J]. Adv Geom, 2010, 10:
[56]  1-630.
[57]  {17}
[58]  7-420.
[59]  {19}
[60]  FRADELIZI M, MEYER M. Some functional inverse Santal\''{o}
[61]  inequalities[J]. Adv Math, 2008, 218: 1430-1452.
[62]  {20}
[63]  FRADELIZI M, MEYER M. Functional inequalities related to Mahler''s
[64]  conjecture[J]. Monatsh Math, 2010, 159: 13-25.
[65]  {21}
[66]  GROEMER H. Geometric Applications of Fourier Series and Spherical
[67]  Harmonics[M]. New York: Cambridge University Press, 1996.
[68]  {22}
[69]  KOLDOBSKY A. Fourier Analysis in Convex Geometry[M]. Providence, RI:
[70]  Amer Math Soc, 2005.
[71]  {23}
[72]  SCHNEIDER R. Convex Bodies: The Brunn-Minkowski Theory[M].
[73]  Cambridge: Cambridge University Press, 1993.
[74]  {24}
[75]  WANG Z, GUO D. Special Functions[M]. Singapore: World Scientific
[76]  Publishing Co, 1989.
[77]  {25}
[78]  ANDREWS G, ASKEY R, ROY R. Special Functions[M]. Cambridge:
[79]  Cambridge Univ Press, 2000.
[80]  {26}
[81]  AKHIEZER N I. The Classical Moment Problem, and Some Related
[82]  Questions in Analysis[M]. Edinburgh: Oliver and Boyd, 1965.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133