4 research outputs found
Quasi-permutable normal operators in octonion Hilbert spaces and spectra
Families of quasi-permutable normal operators in octonion Hilbert spaces are
investigated. Their spectra are studied. Multiparameter semigroups of such
operators are considered. A non-associative analog of Stone's theorem is
proved.Comment: 20 page
Differential equations over octonions
Differential equations with constant and variable coefficients over octonions
are investigated. It is found that different types of differential equations
over octonions can be resolved. For this purpose non-commutative line
integration is used. Such technique is applied to linear and non-linear partial
differential equations in real variables. Possible areas of applications of
these results are outlined.Comment: 50 page