Hypercomplex Differentiabilty and its Applications

Malonek, Helmuth R.

doi:10.1007/978-94-011-2006-7_17

Cited by 10 publications

(18 citation statements)

References 5 publications

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“…[22]), and even that they constitute a basis for the space of monogenic polynomials (as a module over a(n)). In general, the symmetrized product is not associative, and manipulating it can become quite formal.…”

Section: Representation Of 'L In a Space Of Monogenic Functionsmentioning

confidence: 98%

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Monogenic functions and representations of nilpotent Lie groups in quantum mechanics

Cnops

Kisil

1999

Math. Meth. Appl. Sci.

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Section: Representation Of 'L In a Space Of Monogenic Functionsmentioning

confidence: 98%

“…The creation and annihilation operators a> I and a\ I can be represented using symmetric multiplication (see [22]) with the monogenic variable x H , which will be written …”

Section: Representation Of 'L In a Space Of Monogenic Functionsmentioning

confidence: 99%

Monogenic functions and representations of nilpotent Lie groups in quantum mechanics

Cnops

Kisil

1999

Math. Meth. Appl. Sci.

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“…1 ; : : : ; n / is an arbitrary multi-index, are both left and right hypercomplex differentiable or, equivalently, left and right monogenic. Therefore, they can serve as basis for generalized power series as defined also in Malonek (1993).…”

Section: Fueter Polynomialsmentioning

confidence: 99%

“…The idea is to introduce a symmetric product that preserves the monogenicity of the factors. To start with, some relations used in Malonek (1993) for the generalization of power series in terms of E z D .z 1 ; : : : ; z n / 2 H n will be introduced:…”

Section: Fueter Polynomialsmentioning

confidence: 99%

Clifford Analysis and Harmonic Polynomials

Gürlebeck

Sprößig

2013

Handbook of Geomathematics

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This overview gives an insight in the new field of hypercomplex analysis in relation to harmonic analysis. The algebra of complex numbers is replaced by the non-commutative algebra of real quaternions or by Clifford algebras. This contribution is focused on the presentation of an operator calculus on the sphere as well as the discussion of monogenic and holomorphic orthonormal systems of polynomials and special functions on the unit ball and the sphere. Function theoretic elements are lined out. Relations to the Lie algebra SO.3/ are discussed and a corresponding Radon transform is introduced.

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“…This can be done by analogy with the general definition of hypercomplex differentiable functions (see e.g. [17,18]). Here we are giving a modified definition in a more symmetrical way.…”

Section: Biquaternionic Differentiabilitymentioning

confidence: 99%

Biquaternionic Integral Representations for Massive Dirac Spinors in a Magnetic Field and Generalized Biquaternionic Differentiability

Kravchenko¹,

Malonek

Santana³

1996

Math. Meth. Appl. Sci.

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The Dirac equation with a vector potential is considered using a biquaternionic formalism and boundary integral representations for its solutions are obtained. In order to characterize these solutions by a property of local approximability by linearization the corresponding notion of biquaternionic differentiability and its generalization in the sense of Bers (adapted to the spatial case) are given.

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Hypercomplex Differentiabilty and its Applications

Cited by 10 publications

References 5 publications

Monogenic functions and representations of nilpotent Lie groups in quantum mechanics

Monogenic functions and representations of nilpotent Lie groups in quantum mechanics

Clifford Analysis and Harmonic Polynomials

Biquaternionic Integral Representations for Massive Dirac Spinors in a Magnetic Field and Generalized Biquaternionic Differentiability

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