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Regularized Laplaci...
Regularized Laplacian determinants of self-similar fractals
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- Chen, Joe P. (författare)
- Colgate Univ, Hamilton, NY 13346 USA,Colgate Universty, Hamilton, NY, USA
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- Teplyaev, Alexander (författare)
- Univ Connecticut, Storrs, CT 06269 USA,University of Connecticut, Storrs, CT, USA
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- Tsougkas, Konstantinos (författare)
- Uppsala universitet,Matematiska institutionen,Uppsala University, Sweden
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(creator_code:org_t)
- 2017-11-22
- 2018
- Engelska.
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Ingår i: Letters in Mathematical Physics. - : SPRINGER. - 0377-9017 .- 1573-0530. ; 108:6, s. 1563-1579
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Abstract
Ämnesord
Stäng
- We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar fractafolds, in the sense of Strichartz. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of locally self-similar sets such that their complex dimensions are not on the imaginary axis, which allows us to interpret their Laplacian determinant as the regularized product of their eigenvalues. We then investigate a connection between the logarithm of the determinant of the discrete graph Laplacian and the regularized one.
Ämnesord
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Regularized determinant
- Fractal Laplacian
- Spectral zeta functions
- Sierpinski gasket
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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