A unified approach to infinite dimensional integration

Abstract

An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear functionals, as much as possible independent of the underlying topological and measure theoretical structure. Various applications are given, including, next to Schrödinger and diffusion equations, also higher order hyperbolic and parabolic equations.

References in corpus (2)

• Characterization of informational completeness for covariant phase space observables
• Simulating continuous quantum systems by mean field fluctuations

Cited by in corpus (18)

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• Contractivity properties of a quantum diffusion semigroup
• Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians
• Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
• Rapidly Decaying Wigner Functions are Schwartz Functions
• Sobolev Spaces, Schwartz Spaces, and a definition of the Electromagnetic and Gravitational coupling
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