Titlebook: Clifford Analysis and Its Applications; F. Brackx,J. S. R. Chisholm,V. Souček Book 2001 Springer Science+Business Media Dordrecht 2001 Bou

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Book 2001 used and applied to problems inother fields of mathematics, numerical analysis, and mathematicalphysics. recently, the theory has enlarged its scope considerably byincorporating geometrical methods from global analysis on manifoldsand methods from representation theory. New, interesting branches of

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CSR, Sustainability, Ethics & Governancemetric. For anisotropic media two scalar products can be introduced depending on the electric permittivity and magnetic permeability tensors. We show which part of the description of plane electromagnetic waves is independent of scalar products.

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https://doi.org/10.1007/978-3-8349-6202-7al case is played here (in the symplectic case) by Segal-Shale-Weil representation. This representation is infinite-dimensional, so the Harish-Chandra category of . = .(.)-finite modules must be introduced.

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Monogenic Forms of Polynomial Type,ces of the group . with weight λ on an oriented riemannian spin manifold .. For the flat space . = . . there is the Clifford analysis as a natural method for the study of properties of these fields. Their Taylor series are composed from polynomial-type fields, the elements of some finite-dimensional

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Parallel Transport of Algebraic Spinors on Clifford Manifolds,point ., orthonormal basis vector sets define the tangent space and the spin group. The Riemannian and spin connections are defined by imposing covariance under coordinate and spin group transformations. Then the frame field is necessarily parallel transported as a spin vector, subject to both conne

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,A Correspondence of Hyperholomorphic and Monogenic Functions in ℝ4,y e., e. and e.. Any element . in . may be decomposed as . = . + Q. . for quaternions . and .. The Dirac operator in ℝ. is defined by . Leutwiler noticed that the power function . is a solution of the modified Cauchy-Riemann system .which has connections to the hyperbolic metric. We study solutions

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Plane Waves in Premetric Electrodynamics,multivectors and differential forms but no scalar product is necessary. We call it premetric electrodynamics. In this part, the principal equations of the theory can be tackled. The second part concerns solutions of the equations and requires the establishing of a scalar product and, consequently a

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Contact Symplectic Geometry in Parabolic Invariant Theory and Symplectic Dirac Operator,sed with projections onto irreducible components of the target space. Following this general construction, we introduce, inside parabolic geometry (parabolic invariant theory), the symplectic Dirac operator first defined via analytical methods by K.Haberman. The role of the spinor bundle in orthogon