Displaying similar documents to “Rarita-Schwinger type operators on spheres and real projective space”

Fischer decompositions in Euclidean and Hermitean Clifford analysis

Freddy Brackx, Hennie de Schepper, Vladimír Souček (2010)

Archivum Mathematicum

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Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂ ̲ . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂ ̲ J , leading to the system of equations ∂ ̲ f = 0 = ∂ ̲ J f expressing so-called Hermitean monogenicity. The invariance...

A tutorial on conformal groups

Ian Porteous (1996)

Banach Center Publications

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Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to ℝ p , q , the real vector space ℝ p + q , furnished with the quadratic form x ( 2 ) = x · x = - x 1 2 - x 2 2 - . . . - x p 2 + x p + 1 2 + . . . + x p + q 2 , and especially with a description of this group that involves Clifford algebras.

Additive combinations of special operators

Pei Wu (1994)

Banach Center Publications

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This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible...

Twisted spherical means in annular regions in ℂ n and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

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Let Z ( Ann ( r , R ) ) be the class of all continuous functions f on the annulus Ann ( r , R ) in ℂ n with twisted spherical mean f × μ s ( z ) = 0 , whenever z ∈ ℂ n and s > 0 satisfy the condition that the sphere S s ( z ) ⊆ Ann ( r , R ) and ball B r ( 0 ) ⊆ B s ( z ) . In this paper, we give a characterization for functions in Z ( Ann ( r , R ) ) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in ℂ n which improve some of the earlier results.