COMPLEX WEYL SYMBOLS OF THE EXTENDED METAPLECTIC REPRESENTATION OPERATORS

被引：0
作者：
Cahen, Benjamin
机构：
[1] Université de Lorraine, Site de Metz, UFR-MIM, Département de mathématiques, Bâtiment A, 3 rue Augustin Fresnel, BP 45112, METZ Cedex 03
来源：
OPERATORS AND MATRICES | 2024年 / 18卷 / 02期
关键词：
Complex Weyl calculus; Weyl correspondence; Fock space; Bargmann-Fock representation; Berezin quantization; Heisenberg group; extended metaplectic representation; symplectic group; Jacobi group; reproducing kernel Hilbert space; BEREZIN TRANSFORM;
D O I：
10.7153/oam-2024-18-28
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the extended metaplectic representation of the semi-direct product of the Heisenberg group and the symplectic group (the Jacobi group). We give explicit formulas for the Berezin symbols and for the complex Weyl symbols of the corresponding representation operators. Then we deduce formulas for the symbols of the representation operators in the classical Weyl calculus. As an application, we find the classical Weyl symbol of the exponential of an operator whose Weyl symbol is a polynomial on R 2 n of degree 5 2, recovering a result of L. Ho<spacing diaeresis>rmander.
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收藏
页码：457 / 477
页数：2
相关论文
共 30 条
[1]  
[Anonymous], 1985, Grundlehren der mathematischen Wissenschaften Fundamental Principles of Mathematical Sciences
[2]  
Arazy J., 2002, Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei. Matematica e Applicazioni, V13, P165
[3]  
BARGMANN V., 1970, Analytic methods in mathematical physics, P27
[4]   STAR EXPONENTIALS OF THE ELEMENTS OF THE INHOMOGENEOUS SYMPLECTIC LIE-ALGEBRA [J].
BAYEN, F ;
MAILLARD, JM .
LETTERS IN MATHEMATICAL PHYSICS, 1982, 6 (06) :491-497
[5]   DEFORMATION THEORY AND QUANTIZATION .2. PHYSICAL APPLICATIONS [J].
BAYEN, F ;
FLATO, M ;
FRONSDAL, C ;
LICHNEROWICZ, A ;
STERNHEIMER, D .
ANNALS OF PHYSICS, 1978, 111 (01) :111-151
[6]  
Berezin F.A., 1974, MATH USSR IZV, V8, P1109, DOI [10.1070/IM1974v008n05ABEH002140, DOI 10.1070/IM1974V008N05ABEH002140]
[7]  
Berezin FA., 1975, Mathematics of the USSR-Izvestiya, V9, P341, DOI DOI 10.1070/IM1975V009N02ABEH001480
[8]  
Berndt R., 1998, Progr. Math., V163
[9]  
CAHEN B., 2022, Nihonkai Math. J., V33, P61
[10]  
CAHEN B., 2018, Rend. Semin. Mat. Univ. Politec. Torino, V76, P63
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