Photo from wikipedia
Let $$f_\omega (z)=\sum \nolimits _{j=0}^{\infty }\chi _j(\omega ) a_j z^j$$ be a transcendental random entire function, where $$\chi _j(\omega )$$ are independent and identically distributed random variables defined on a… Click to show full abstract
Let $$f_\omega (z)=\sum \nolimits _{j=0}^{\infty }\chi _j(\omega ) a_j z^j$$ be a transcendental random entire function, where $$\chi _j(\omega )$$ are independent and identically distributed random variables defined on a probability space $$(\Omega , \mathcal {F}, \mu )$$ . In this paper, we study a family of random entire functions, which includes Gaussian, Rademacher, and Steinhaus entire functions. Then we prove that if two random entire functions in this family share two distinct complex numbers counting multiplicities, then they are identically equal.
Journal Title: Complex Analysis and Operator Theory
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!