Geodesic
Beta functions of Bruhat--Tits buildings and deformation of $l^2$
Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1775-1805

Voir la notice de l'article provenant de la source Math-Net.Ru

For the space $\operatorname{Lat}_n$ of all lattices in an $n$-dimensional $p$-adic linear space an analogue of the matrix beta function is constructed; this beta function can degenerate to the Tamagawa zeta function. An analogue of Berezin kernels for $\operatorname{Lat}_n$ is proposed. Conditions for the positive-definiteness of these kernels and an explicit Plancherel's formula are obtained. 
@article{SM_2003_194_12_a1,
     author = {Yu. A. Neretin},
     title = {Beta functions of {Bruhat--Tits} buildings and deformation of $l^2$},
     journal = {Sbornik. Mathematics},
     pages = {1775--1805},
     publisher = {mathdoc},
     volume = {194},
     number = {12},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_12_a1/}
}
TY  - JOUR
AU  - Yu. A. Neretin
TI  - Beta functions of Bruhat--Tits buildings and deformation of $l^2$
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 1775
EP  - 1805
VL  - 194
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_12_a1/
LA  - en
ID  - SM_2003_194_12_a1
ER  - 
%0 Journal Article
%A Yu. A. Neretin
%T Beta functions of Bruhat--Tits buildings and deformation of $l^2$
%J Sbornik. Mathematics
%D 2003
%P 1775-1805
%V 194
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2003_194_12_a1/
%G en
%F SM_2003_194_12_a1
Yu. A. Neretin. Beta functions of Bruhat--Tits buildings and deformation of $l^2$. Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1775-1805. http://geodesic.mathdoc.fr/item/SM_2003_194_12_a1/