Monogenic Functions in Infinite-Dimensional Vector Spaces with Commutative Multiplication and Harmonic Vectors

Explore monogenic functions in infinite-dimensional vector spaces with commutative multiplication and harmonic vectors in this 49-minute inaugural lecture from the HyperComplex Seminar 2023. Delve into the study of special topological vector spaces with commutative multiplication for certain elements, motivated by the need to describe spatial harmonic functions as components of hypercomplex monogenic functions. Learn about Gâteaux-differentiable monogenic functions and their relationship to spatial harmonic functions. Examine the connections between monogenic functions and harmonic vectors in three-dimensional real space, and discover sufficient conditions for infinite monogeneity. Gain insights into this field of study, where the validity of the Cauchy integral formula for monogenic functions remains an open problem, distinguishing it from classical complex analysis.