Gaussian Measures on Separable Hilbert Spaces and Applications - 2004

Stefania Maniglia, Abdelaziz Rhandi Full Version (PDF)
(Quaderni di Matematica, 1 / 2004)
QdM_1_2004 - Cover ISBN: 88-8305-010
e-ISBN: 88-8305-011-8 

The aim of these lecture notes is to present some basic facts and ideas of the theory of Gaussian measures on infinite dimensional Hilbert spaces and to show to the reader how this theory can be applied to solve the infinite dimensional heat equation and, more generally, its perturbations by a linear drift term.

In particular, the Cameron-Martin theorem will be useful to obtain regularity properties of the semigroup generated by the Gross-Laplacian and the Ornstein-Uhlenbeck semigroup.

These notes originated from a course given by the second author at the University of Lecce in May 2002 and at the University of Halle-Wittenberg in May 2003.


Table Of Contents


Preface     PDF
Stefania Maniglia, Abdelaziz Rhandi iii

Gaussian measures on Hilbert spaces     PDF
Stefania Maniglia, Abdelaziz Rhandi 1-24

Heat equations in Hilbert spaces     PDF
Stefania Maniglia, Abdelaziz Rhandi 25-44

The Ornstein-Uhlenbeck semigroup     PDF
Stefania Maniglia, Abdelaziz Rhandi 45-72

Appendix     PDF
Stefania Maniglia, Abdelaziz Rhandi 73-80

Bibliography     PDF
Abdelaziz Rhandi, Stefania Maniglia 81

Index     PDF
Abdelaziz Rhandi, Stefania Maniglia


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