Spectral theory of super-differential operators of quaternion and octonion variables

DOI10.1007/s00006-010-0238-4zbMath1238.47028OpenAlexW2072541294MaRDI QIDQ537487

Wolfgang Sprössig, Sergey V. Ludkovsky

Publication date: 20 May 2011

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-010-0238-4

zbMATH Keywords

quaternionscompact operatorsoctonionssuper-differential operators

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Functions of hypercomplex variables and generalized variables (30G35) Linear operators defined by compactness properties (47B07) General theory of ordinary differential operators (47E05) Ordinary differential equations in the complex domain (34M99)

Related Items (12)

Schauder bases in Dirac modules over quaternions ⋮ Physical quantities and spatial parameters in the complex octonion curved space ⋮ Analytic extensions of functions of Cayley-Dickson variables ⋮ Unbounded normal operators in octonion Hilbert spaces and their spectra ⋮ Four interactions in the sedenion curved spaces ⋮ On a class of right linearly differentiable functions of Cayley-Dickson variables ⋮ Existence of an invariant measure on a topological quasigroup ⋮ Contrastive analysis of two energy gradients in the ultra-strong magnetic fields ⋮ Completions and homomorphisms of infinite dimensional Cayley–Dickson algebras ⋮ Quasi-permutable normal operators in octonion Hilbert spaces and spectra ⋮ Cohomology theory of nonassociative algebras with metagroup relations ⋮ Spectral representations of operators in Hilbert spaces over quaternions and octonions

Cites Work

• Differentiable functions of Cayley-Dickson numbers and line integration
• Functions of several Cayley-Dickson variables and manifolds over them
• Stochastic processes on geometric loop groups, diffeomorphism groups of connected manifolds, and associated unitary representations
• Algebras of operators in Banach spaces over the quaternion skew field and the octonion algebra
• Differentiable functions of quaternion variables.
• An affine connection in an almost quaternion manifold
• Extension of C ∞ Functions Defined in a Half Space
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