arXiv subjects

Alexander Kheyfits

Publications and source records attributed to Alexander Kheyfits.

4 recordsLinked to original sources

arXiv2019

The area integral and boundary values of octonion-valued monogenic functions

We introduce the Area Integral for octonion-valued monogenic functions in the half-space. It is used to prove the existence of the non-tangential boundary values almost everywhere and of the normal boundary values at a given boundary point for these classes of functions. It is also proved that the non-tangential limit for the scalar component of a monogenic function and those limits for all of its other seven components exist or not exist simultaneously. It turns out that non-commutativity and non-associativity of octonions in certain problems can be circumvented by making use of P. Stein method and employing subharmonic functions.

math.CV↗

arXiv2018

Closed-form solution of polynomial equations

Integral Cauchy theorem is used to derive closed-form expressions of the roots of a univariate polynomial of any degree as integrals of elementary functions.

math.CV↗

arXiv2017

Another Incarnation of the Lambert W Function

The Lambert W function was introduced by Euler in 1779, but was not well-known until it was implemented in Maple, and the seminal paper of Corless, Gonnet, Hare, Jeffrey and Khuth was published in 1996. In this note we describe a simple problem, which can be straightforwardly solved in terms of the W function.

math.CA↗

arXiv2012

A Representation of the Associated Legendre Functions of the First Kind on the Cut as the Mellin Transformation of the Riesz Kernel

A Mellin transform representation is derived for the associated Legendre functions of the first kind on the cut

math.CV↗