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Continuous groups with antilinear operations of the form $G+a_0G$, where $G$ denotes a linear Lie group, and $a_0$ is an antilinear operation which fulfills the condition $a^2_0=pm 1$, were defined and their matrix algebras were investigated in cite{Kocinski4}. In this paper infinitesimal-operator algebras are defined for any group of the form $G+a_0G$, and their properties are determined.
Continuous groups of the form: $G+a_0G$ are defined, where $G$ denotes a Lie group and $a_0$ denotes an antilinear operation which fullfils the condition $a^2_0=pm 1$. The matrix algebras connected with the groups $G+a_0G$ are defined. The structural
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
We consider a Dirac operator with a dislocation potential on the real line. The dislocation potential is a fixed periodic potential on the negative half-line and the same potential but shifted by real parameter $t$ on the positive half-line. Its spec
Based on the ideology of the Maslovs complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. T
We study the spectrum of the linear operator $L = - partial_{theta} - epsilon partial_{theta} (sin theta partial_{theta})$ subject to the periodic boundary conditions on $theta in [-pi,pi]$. We prove that the operator is closed in $L^2([-pi,pi])$ wit