Isospektral: Perbedaan antara revisi

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Revisi terkini sejak 14 April 2023 18.13

Dalam matematika, dua operator linear disebut isospektral atau kospektral jika mereka memiliki spektrum yang sama. Secara keseluruhan, mereka memiliki beberapa set dari nilai eigen, saat itu dihitung dengan multiplisita.

Teori operator isospektral bergantung pada tanda yang berbeda pada apakah ruang tersebut adalah dimensi terbatas atau tak terbatas. Dalam dimensi terbatas, hal tersebut secara esensial sejalan dengan matriks-matriks persegi.

Referensi

Bérard, Pierre (1988–1989), Variétés riemanniennes isospectrales non isométriques, exposé 705 (PDF), Séminaire Bourbaki, 31
Brooks, Robert (1988), "Constructing Isospectral Manifolds", American Mathematical Monthly, Mathematical Association of America, 95 (9): 823–839, doi:10.2307/2322897, JSTOR 2322897
Buser, Peter (1986), "Isospectral Riemann surfaces" (PDF), Annales de l'Institut Fourier, 36: 167–192, doi:10.5802/aif.1054
Buser, Peter; Conway, John; Doyle, Peter; Semmler, Klaus-Dieter (1994), "Some planar isospectral domains", Int. Math. Res. Notices: 391–400, diarsipkan dari versi asli tanggal 2019-02-20, diakses tanggal 2017-09-27
McKean, H. P. (1972), "Selberg's trace formula as applied to a compact Riemann surface", Comm. Pure Appl. Math., 25 (3): 225–246, doi:10.1002/cpa.3160250302
Maclachlan, C.; Reid, Alan W. (2003), The Arithmetic of Hyperbolic 3-manifolds, Springer, hlm. 383–394, ISBN 0387983864 ,
Milnor, John (1964), "Eigenvalues of the Laplace operator on certain manifolds", Proc. Natl. Acad. Sci. USA, 51 (4): 542, doi:10.1073/pnas.51.4.542, PMC 300113 , PMID 16591156
Schueth, D. (1999), "Continuous families of isospectral metrics on simply connected manifolds", Annals of Mathematics, 149 (1): 287–308, doi:10.2307/121026, JSTOR 121026
Selberg, Atle (1956), "Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series", J. Indian Math. Soc., 20: 47–87
Sunada, T. (1985), "Riemannian coverings and isospectral manifolds", Annals of Mathematics, 121 (1): 169–186, doi:10.2307/1971195, JSTOR 1971195
Vignéras, Marie-France (1980), "Variétés riemanniennes isospectrales et non isométriques", Annals of Mathematics, Annals of Mathematics, 112 (1): 21–32, doi:10.2307/1971319, JSTOR 1971319
Wolpert, Scott (1977), "The eigenvalue spectrum as moduli for compact Riemann surfaces" (PDF), Bull. Amer. Math. Soc., 83 (6): 1306–1308, doi:10.1090/S0002-9904-1977-14425-X
Wolpert, Scott (1979), "The length spectra as moduli for compact Riemann surfaces", Annals of Mathematics, 109 (2): 323–351, doi:10.2307/1971114, JSTOR 1971114

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