Geodesic
The periodic Fock bundle
Algebra i analiz, Tome 3 (1991) no. 5, pp. 135-154 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Fock bundle is an Hermitean vector bundle over Siegel's generalized upper halfplane, the fibers of which can be realized as Hilbert spaces of entire functions. In this paper a “periodic” version of the Fock bundle is constructed, that is, we factor the fibers of the (usual) Fock bundle by a maximal isotropic discrete subgroup of the underlying symplectic vector space. Applications to theta functions are obtained. In fact, it is our intention to work out, in a subsequent publication, major parts of the classical theory of theta functions on the basis ofthe corresponding “doubly periodic” object, obtained by instead factoring by a symplectic lattice.
Keywords: Fock space, Heisenberg group, Siegel's generalized upper halfplane, reproducing kernel, theta function, Hermitean vector bundle, connection. 
@article{AA_1991_3_5_a5,
     author = {Jaak Peetre},
     title = {The periodic {Fock} bundle},
     journal = {Algebra i analiz},
     pages = {135--154},
     year = {1991},
     volume = {3},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_1991_3_5_a5/}
}
TY  - JOUR
AU  - Jaak Peetre
TI  - The periodic Fock bundle
JO  - Algebra i analiz
PY  - 1991
SP  - 135
EP  - 154
VL  - 3
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/AA_1991_3_5_a5/
LA  - en
ID  - AA_1991_3_5_a5
ER  - 
%0 Journal Article
%A Jaak Peetre
%T The periodic Fock bundle
%J Algebra i analiz
%D 1991
%P 135-154
%V 3
%N 5
%U http://geodesic.mathdoc.fr/item/AA_1991_3_5_a5/
%G en
%F AA_1991_3_5_a5
Jaak Peetre. The periodic Fock bundle. Algebra i analiz, Tome 3 (1991) no. 5, pp. 135-154. http://geodesic.mathdoc.fr/item/AA_1991_3_5_a5/