An introduction to $BV$ functions in Wiener spaces
M. Miranda Jr, M. Novaga, D. Pallara
TL;DR
This paper introduces the foundational concepts of functions of bounded variation and finite perimeter sets within the context of abstract Wiener spaces, expanding the mathematical framework for analysis in infinite-dimensional probability spaces.
Contribution
It develops the theoretical underpinnings of BV functions and finite perimeter sets specifically tailored for abstract Wiener spaces, a novel extension of classical finite-dimensional theory.
Findings
Established the basic properties of BV functions in Wiener spaces
Defined sets of finite perimeter in the infinite-dimensional setting
Extended classical BV theory to abstract Wiener spaces
Abstract
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.
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Taxonomy
Topicsadvanced mathematical theories · Mathematical Analysis and Transform Methods · Advanced Mathematical Modeling in Engineering