I am interested in Hermite polynomials for my study of Ito-Wiener expansion, as they are mentioned to have close relations with each other, but I'm acquainted with the former a little bit only, especially in the framework of Quantum Mechanics. So I have a strong need for a good description of Hermite polynomials in relation with Measure theory in Hilbert spaces.
There is an extensive bibliography of Hermite polynomial references in Hermite Polynomial. However, my go-to reference for most functions is K. Oldham, J. Myland, & J. Spanier, An Atlas of Functions, Springer . Chapter 24 covers the Hermite polynomials.