Infinite dimensional integration of oscillatory type and applications

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 15:00

Relatore:

• Sonia Mazzucchi (Dipartimento di Matematica Università di Trento)
  
   

Abstract:

In this talk I shall give an overview of alternative integration techniques on infinite dimensional spaces based on the concept of integral as a linear functional, instead of the concept of measure, on which the Lebesgue’s ”traditional” integration theory is based. This alternative approach is necessary in the cases where a sigma-additive measure with given finite dimensional approximations cannot exist. The main application of these techniques is the mathematical definition of Feynman path integrals and the construction of a functional integral representation of the solution of the Schrödinger equation, nevertheless I shall point out that the scope of this theory goes beyond Feynman integration and it can find interesting applications in the study of more general dynamical systems.

Referente: Andrea Pugliese