3 papers
math.HO2026
Infinitesimals inside the Familiar Field of Complex Numbers
Todor D. Todorov
We show that the field of complex numbers contains non-zero infinitesimals by observing that contains non-Archimedean subfields. Our observation is based on…
math.FA2024
An Embedding of Schwartz Distributions in the Algebra of Asymptotic Functions
M. Oberguggenberger, T. Todorov
We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, calle…
math.FA2024
Non-Standard Version of Egorov Algebra of Generalized Functions
Todor D. Todorov
We consider a non-standard version of Egorov's algebra of generalized functions, with improved properties of the generalized scalars and embedding of the Schwartz distributions com…