### "On the Equivalence of Measures on Loop Space" by Vikram Srimurthy.

(UCSD Thesis, June 1999)

The manuscript is available as a DVI file or as a PDF file.

Abstract

Let $K$ be a simply-connected compact Lie Group equipped with an $Ad_{K}$% -invariant inner product on the Lie Algebra $\frak{K}$, of $K$. Given this data, there is a well known left invariant ''$H^{1}$-Riemannian structure'' on $L\left( K\right)$ (the infinite dimensional group of continuous based loops in K), as well as a heat kernel $\nu _{T}\left( k_{0},\cdot \right)$associated with the Laplace-Beltrami operator on $L\left( K\right)$. Here $% T>0$, $k_{0}\in L\left( K\right)$, and $\nu _{T}\left( k_{0},\cdot \right)$ is a certain probability measure on $L\left( K\right)$. In this paper we show that $\nu _{1}\left( e,\cdot \right)$ is equivalent to Pinned Wiener Measure on $K$ on $\frak{G}_{s_{0}}\equiv \sigma \left\langle x_{t}:t\in \left[ 0,s_{0}\right] \right\rangle$ (the $\sigma$-algebra generated by truncated loops up to time'' $s_{0}$)

June, 1999

The following two papers constitute (together) a refined version of Srimurthy's is thesis.

 "On the Equivalence of Measures on Loop Space" by Vikram Srimurthy.

This manuscript is available as a DVI  file or as a PDF file.

 "Absolute continuity of Heat Kernel measure with pinned Wiener measure on Loop groups" by Bruce K. Driver and  Vikram Srimurthy.

This manuscript is available as a DVI I file or as a PDF file.

 08/15/2016 02:53 PM