**Contemporary Mathematics**

Volume: 317;
2003;
224 pp;
Softcover

MSC: Primary 60; 28; 46; 58; 31; 62; 81;

Print ISBN: 978-0-8218-3202-8

Product Code: CONM/317

List Price: $57.00

Individual Member Price: $45.60

**Electronic ISBN: 978-0-8218-7907-8
Product Code: CONM/317.E**

List Price: $57.00

Individual Member Price: $45.60

# Finite and Infinite Dimensional Analysis in Honor of Leonard Gross

Share this page *Edited by *
*Hui-Hsiung Kuo; Ambar N. Sengupta*

This book contains the proceedings of the special session in honor of Leonard
Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The
speakers were specialists in a variety of fields, and many were Professor
Gross's former Ph.D. students and their descendants.

Papers in this volume present results from several areas of mathematics. They
illustrate applications of powerful ideas that originated in Gross's work and
permeate diverse fields. Topics include stochastic partial differential
equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat
kernels, and some applications.

The volume should be useful to graduate students and researchers. It provides
perspective on current activity and on central ideas and techniques in the
topics covered.

#### Table of Contents

# Table of Contents

## Finite and Infinite Dimensional Analysis in Honor of Leonard Gross

- Contents v6 free
- Preface vii8 free
- Speakers ix10 free
- Ph.D. students of L. Gross xi12 free
- Meixner classes and the square of white noise 114 free
- Strong Feller properties for distorted Brownian motion and applications to finite particle systems with singular interactions 1528
- 1. Introduction 1528
- 2. An elliptic regularity result and its consequences 1831
- 3. Construction of the semigroup and resolvent of kernels 2033
- 4. Construction of the associated diffusion process 2437
- 5. Solution to the stochastic equation 2841
- 6. Applications to stochastic dynamics 3043
- Acknowledgement 3346
- References 3346

- Market price of risk and random field driven models of term structure: A space-time change of measure look 3750
- Gaussian and Poisson white noises with related characterization theorems 4558
- Analysis of Wiener measure on path and loop groups 5770
- Stochastic differential equations on noncommutative L2 87100
- The Segal–Bargmann transform and the Gross ergodicity theorem 99112
- Sharp bounds for the heat kernel on certain symmetric spaces of non-compact type 117130
- Laplacians in white noise analysis 137150
- On Dirichlet spaces over convex sets in infinite dimensions 143156
- Information capacity of quantum channels 157170
- The Riesz representation theorem on infinite dimensional spaces 163176
- Asymptotic behavior in heat kernel analysis on manifolds 179192
- Complex stochastic calculus 193206
- Recent results and open problems in Segal–Bargmann analysis 203216
- A new Heisenberg inequality for white noise analysis 215228

#### Readership

Research mathematicians interested in probability and analysis.