Rocky Mountain Journal of Mathematics

On the spectrum of spherical Dirac-type operators

N. Anghel

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Abstract

We use polynomial Dirac spinors associated to Euclidean Dirac-type operators and separation of variables to investigate the spectral theory of certain spherical Dirac-type operators. While the spectral theories of our main examples, the spherical Dirac and Laplace-Beltrami operators, are known, this is the first time they are treated together, in a unified manner. In particular, the multiplicities of these spectra, a topic difficult to negotiate in many previous treatments, are presented in simple closed form.

Article information

Source
Rocky Mountain J. Math., Volume 43, Number 6 (2013), 1825-1856.

Dates
First available in Project Euclid: 25 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1393336658

Digital Object Identifier
doi:10.1216/RMJ-2013-43-6-1825

Mathematical Reviews number (MathSciNet)
MR3178445

Zentralblatt MATH identifier
1284.53047

Subjects
Primary: 53C27: Spin and Spin$^c$ geometry 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Secondary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

Keywords
Euclidean Dirac operator polynomial spinor graded Clifford representation spherical Dirac operator separation of variables spectrum multiplicity classical Dirac-type operator Gauss-Bonnet-type operator

Citation

Anghel, N. On the spectrum of spherical Dirac-type operators. Rocky Mountain J. Math. 43 (2013), no. 6, 1825--1856. doi:10.1216/RMJ-2013-43-6-1825. https://projecteuclid.org/euclid.rmjm/1393336658


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