Feynman's operational calculi for noncommuting operators: The monogenic calculus

DOI10.1007/BF03042315zbMath1096.47501OpenAlexW1965239337MaRDI QIDQ1431046

Gerald W. Johnson, Brian R. F. Jefferies

Publication date: 27 May 2004

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

Full work available at URL: https://doi.org/10.1007/bf03042315

zbMATH Keywords

Clifford algebraBanach module\(\mu\)-joint spectrum\(n\)-tuples of linear operators

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Functional calculus for linear operators (47A60) Spectral sets of linear operators (47A25) Functional calculus in topological algebras (46H30)

Related Items (11)

Feynman's operational calculus with arbitrary measures: an evolution equation in the general case and examples ⋮ Two approaches to the use of unbounded operators in Feynman's operational calculus ⋮ Measure decomposing disentangling in Feynman's operational calculus ⋮ Weak convergence and vector-valued functions: Improving the stability theory of Feynman's operational calculi ⋮ Weak convergence and Banach space-valued functions: improving the stability theory of Feynman's operational calculi ⋮ Feynman's operational calculi: Methods for iterative disentangling ⋮ Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a \((C_0)\) semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time-dependent setting ⋮ Feynman's operational calculi: Disentangling away from the origin ⋮ Stability properties for Feynman's operational calculus in the combined continuous/discrete setting ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time independent setting

Cites Work

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• Feynman's operational calculi for noncommuting operators: definitions and elementary properties
• Feynman's operational calculus for families of noncommuting operators: tensor products, ordered supports, and the disentangling of an exponential factor
• The Weyl functional calculus
• The Weyl calculus and Clifford analysis
• Lacunas in the Support of the Weyl Calculus for Two Hermitian Matrices
• FEYNMAN'S OPERATIONAL CALCULI FOR NONCOMMUTING OPERATORS: SPECTRAL THEORY
• Functions of Several Self-Adjoint Operators

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