Extending the Set of Quadratic Exponential Vectors

TL;DR

This paper extends the square of white noise algebra to higher-dimensional test functions and demonstrates the existence of exponential vectors in the Fock representation for functions bounded by 1/2.

Contribution

It generalizes the algebraic framework to a broader class of functions and establishes conditions for exponential vector existence in the Fock space.

Findings

Extended the white noise algebra to bounded square-integrable functions on R^d.

Proved exponential vectors exist in the Fock representation for functions bounded by 1/2.

Broadened the mathematical foundation for white noise analysis.

Abstract

We extend the square of white noise algebra over the step functions on R to the test function space of bounded square-integrable functions on R^d, and we show that in the Fock representation the exponential vectors exist for all test functions bounded by 1/2.