On the eigenfunction expansion of the Laplace-Beltrami operator in hyperbolic space

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Date

2015

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Taylor & Francis Ltd

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

We describe the spectral projection of the Laplace-Beltrami operator in n-dimensional hyperbolic space by studying its resolvent as an analytic operator-valued function and applying the technique of contour integration. As a result an integral formula is established for the associated Legendre function

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hyperbolic space, Laplace-Beltrami operator, spectral projection, eigenfunction expansion, associated Legendre function

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Volume

60

Issue

10

Start Page

1309

End Page

1326

URI

https://doi.org/10.1080/17476933.2015.1012163
 https://hdl.handle.net/20.500.14411/785

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