Octonion measures for solutions of PDEs

DOI10.1007/s00006-020-01062-yzbMath1441.35158OpenAlexW3033408195WikidataQ114232381 ScholiaQ114232381MaRDI QIDQ2190820

Sergey V. Ludkovsky

Publication date: 22 June 2020

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

Full work available at URL: https://doi.org/10.1007/s00006-020-01062-y

zbMATH Keywords

Markov processhypercomplex

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Stochastic integrals (60H05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Higher-order hyperbolic systems (35L55) Second-order parabolic equations (35K10) Higher-order parabolic equations (35K25) Nonassociative algebras satisfying other identities (17A30) Quadratic algebras (but not quadratic Jordan algebras) (17A45)

Cites Work

• Convergence in \(L^{p}\) for Feynman path integrals
• Line integration of Dirac operators over octonions and Cayley-Dickson algebras
• Noncommutative, quasi-conformal integral transforms over quaternions and octonions
• Differentiable functions of Cayley-Dickson numbers and line integration
• Functions of several Cayley-Dickson variables and manifolds over them
• Differentiable functions of quaternion variables.
• Quaternionic analysis and elliptic boundary value problems
• Two-sided Laplace transform over Cayley-Dickson algebras and its applications
• Feynman integration over octonions with application to quantum mechanics
• Integration by parts formulas for analytic Feynman integrals of unbounded functionals
• Functional Integration and Partial Differential Equations. (AM-109)
• The octonions
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