On the index of pseudo-differential operators on compact Lie groups

被引：0
|
作者：
Cardona, Duvan [1 ]
机构：
[1] Pontificia Univ Javeriana, Dept Math, Bogota, Colombia
来源：
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2019年 / 10卷 / 02期
关键词：
Index theorem; Elliptic operator; Compact Lie group; Representation theory;
D O I：
10.1007/s11868-018-0261-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we study the analytical index of pseudo-differential operators by using the notion of (infinite dimensional) operator-valued symbols (in the sense of Ruzhansky and Turunen). Our main tools will be the McKean-Singer index formula together with the operator-valued functional calculus developed here.
引用
收藏
页码：285 / 305
页数：21
相关论文
共 50 条
  • [21] CHARACTERIZATIONS, ADJOINTS AND PRODUCTS OF NUCLEAR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT AND HAUSDORFF GROUPS
    Ghaemi, M. B.
    Jamalpourbirgani, M.
    Wong, M. W.
    [J]. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2017, 79 (04): : 207 - 220
  • [22] Schatten class and nuclear pseudo-differential operators on homogeneous spaces of compact groups
    Kumar, Vishvesh
    Mondal, Shyam Swarup
    [J]. MONATSHEFTE FUR MATHEMATIK, 2022, 197 (01): : 149 - 176
  • [23] Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
    Ruzhansky, Michael
    Turunen, Ville
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2013, 2013 (11) : 2439 - 2496
  • [24] Pseudo-differential operators on finite Abelian groups
    Molahajloo, Shahla
    Wong, K. L.
    [J]. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2015, 6 (01) : 1 - 9
  • [25] Pseudo-differential operators on finite Abelian groups
    Shahla Molahajloo
    K. L. Wong
    [J]. Journal of Pseudo-Differential Operators and Applications, 2015, 6 : 1 - 9
  • [26] Pseudo-differential extension for graded nilpotent Lie groups
    Ewert, Eske
    [J]. DOCUMENTA MATHEMATICA, 2023, 28 : 1323 - 1379
  • [27] Calculus of Pseudo-Differential Operators and a Local Index of Dirac Operators
    Iwasaki, Chisato
    [J]. PSEUDO-DIFFERENTIAL OPERATORS: ANALYSIS, APPLICATIONS AND COMPUTATIONS, 2011, 213 : 123 - 136
  • [28] PSEUDO-DIFFERENTIAL OPERATORS
    HORMANDE.L
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1965, 18 (03) : 501 - &
  • [29] AFFINE LIE ALGEBRAS AND PSEUDO-DIFFERENTIAL OPERATORS OF INFINITE ORDER
    Lesfari, A.
    [J]. MATHEMATICAL REPORTS, 2012, 14 (01): : 43 - 69
  • [30] Pseudo-Differential Operators
    Yuan, Wen
    Sickel, Winfried
    Yang, Dachun
    [J]. MORREY AND CAMPANATO MEET BESOV, LIZORKIN AND TRIEBEL, 2010, 2005 : 137 - 146
12345