5 citations · 9 across the 6 of their papers we have counts for
6 papers
On signed generators of groups and algebras
Jerzy Szulga
Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the a…
Algebraic structures spanned by differential-like operators on toy Fock spaces
Jerzy Szulga
We study multiplicative systems of linear mappings acting on the toy Fock space, a.k.a.\ Rademacher chaos or Walsh-Fourier series, related to the creation, annihilation, and conser…
Lorentz transformation from an elementary point of view
Arkadiusz Jadczyk, Jerzy Szulga
Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $…
A Comment on 'On the Rotation Matrix in Minkowski Space-time' by Ozdemir and Erdogdu
Arkadiusz Jadczyk, Jerzy Szulga
We comment on the article by M. Ozdemir and M. Erdogdu. We indicate that the exponential map onto the Lorentz group can be obtained in two elementary ways. The first way utilizes a…
Contraction and decoupling inequalities for multilinear forms and u-statistics
V. de la Pena, Stephen J. Montgomery-Smith, Jerzy Szulga
We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangeme…
Infinite order decoupling of random chaoses in Banach space
Jerzy Szulga
We prove a number of decoupling inequalities for nonhomogeneous random polynomials with coefficients in Banach space. Degrees of homogeneous components enter into comparison as exp…