메뉴 건너뛰기




Volumn 178, Issue 2, 1997, Pages 169-183

Duality and singular continuous spectrum in the almost Mathieu equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0002638383     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02392693     Document Type: Article
Times cited : (104)

References (27)
  • 1
    • 0001259850 scopus 로고
    • On a problem of Weyl in the theory of Sturm-Liouville equations
    • ARONSZAJN, N., On a problem of Weyl in the theory of Sturm-Liouville equations. Amer. J. Math., 79 (1957), 597-610.
    • (1957) Amer. J. Math. , vol.79 , pp. 597-610
    • Aronszajn, N.1
  • 2
    • 0000519980 scopus 로고
    • The new concept of transitions by breaking of analyticity in a crystallographic model
    • (Oxford, 1978), p Springer Ser. Solid-State Sci., 8. Springer-Verlag, Berlin-New York
    • AUBRY, S., The new concept of transitions by breaking of analyticity in a crystallographic model, in Solitons and Condensed Matter Physics (Oxford, 1978), pp. 264-277. Springer Ser. Solid-State Sci., 8. Springer-Verlag, Berlin-New York, 1978.
    • (1978) Solitons and Condensed Matter Physics , pp. 264-277
    • Aubry, S.1
  • 3
    • 0001215377 scopus 로고
    • Analyticity breaking and Anderson localization in incommensurate lattices
    • AUBRY, S. & ANDRE, G., Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Israel Phys. Soc., 3 (1980), 133-140.
    • (1980) Ann. Israel Phys. Soc. , vol.3 , pp. 133-140
    • Aubry, S.1    Andre, G.2
  • 4
    • 84966202323 scopus 로고
    • Singular continuous spectrum for a class of almost periodic Jacobi matrices
    • AVRON, J. & SIMON, B., Singular continuous spectrum for a class of almost periodic Jacobi matrices. Bull. Amer. Math. Soc., 6 (1982), 81-85.
    • (1982) Bull. Amer. Math. Soc. , vol.6 , pp. 81-85
    • Avron, J.1    Simon, B.2
  • 5
    • 84972566320 scopus 로고
    • Almost periodic Schrödinger operators, II. The integrated density of states
    • _ Almost periodic Schrödinger operators, II. The integrated density of states. Duke Math. J., 50 (1983), 369-391.
    • (1983) Duke Math. J. , vol.50 , pp. 369-391
  • 6
    • 0001723647 scopus 로고
    • A metal-insulator transition for the almost Mathieu model
    • BELLISSARD, J., LIMA, R. & TESTARD, D., A metal-insulator transition for the almost Mathieu model. Comm. Math. Phys., 88 (1983), 207-234.
    • (1983) Comm. Math. Phys. , vol.88 , pp. 207-234
    • Bellissard, J.1    Lima, R.2    Testard, D.3
  • 7
    • 0040258931 scopus 로고
    • A quantum particle in a one-dimensional deformed lattice. Estimates of lacunae dimension in the spectrum
    • Russian
    • BELOKOLOS, E. D., A quantum particle in a one-dimensional deformed lattice. Estimates of lacunae dimension in the spectrum. Teoret. Mat. Fiz., 25 (1975), 344-57 (Russian).
    • (1975) Teoret. Mat. Fiz. , vol.25 , pp. 344-357
    • Belokolos, E.D.1
  • 8
    • 0040258907 scopus 로고
    • A generalized spectral duality theorem
    • CHOJNACKI, W., A generalized spectral duality theorem. Comm. Math. Phys., 143 (1992), 527-544.
    • (1992) Comm. Math. Phys. , vol.143 , pp. 527-544
    • Chojnacki, W.1
  • 9
    • 0001180437 scopus 로고
    • Purely absolutely continuous spectrum for almost Mathieu operators
    • CHULAEVSKY, V. & DELYON, F., Purely absolutely continuous spectrum for almost Mathieu operators. J. Statist. Phys.. 55 (1989), 1279-1284.
    • (1989) J. Statist. Phys. , vol.55 , pp. 1279-1284
    • Chulaevsky, V.1    Delyon, F.2
  • 10
    • 0001091673 scopus 로고
    • Almost periodic schrödinger operators, III. The absolutely continuous spectrum in one dimension
    • DEIFT, P. & SIMON, B., Almost periodic Schrödinger operators, III. The absolutely continuous spectrum in one dimension. Comm. Math. Phys., 90 (1983), 389-411.
    • (1983) Comm. Math. Phys. , vol.90 , pp. 389-411
    • Deift, P.1    Simon, B.2
  • 11
    • 36149032983 scopus 로고
    • Absence of localization for the almost Mathieu equation
    • DELYON, F., Absence of localization for the almost Mathieu equation. J. Phys. A, 20 (1987), L21-L23.
    • (1987) J. Phys. A , vol.20
    • Delyon, F.1
  • 12
    • 34250407352 scopus 로고
    • The one-dimensional Schrödinger equation with a quasiperiodic potential
    • DINABURG, E. & SINAI, YA., The one-dimensional Schrödinger equation with a quasiperiodic potential. Functional Anal. Appl., 9 (1975), 279-289.
    • (1975) Functional Anal. Appl. , vol.9 , pp. 279-289
    • Dinaburg, E.1    Sinai, Ya.2
  • 13
    • 84981761432 scopus 로고
    • On the perturbation of the spectra
    • DONOGHUE, W., On the perturbation of the spectra. Comm. Pure Appl. Math., 18 (1965), 559-579.
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 559-579
    • Donoghue, W.1
  • 14
    • 0002234361 scopus 로고
    • Localization for a class of one-dimensional quasi-periodic Schrödinger operators
    • FRÖHLICH, J., SPENCER, T. & WITTWER, P., Localization for a class of one-dimensional quasi-periodic Schrödinger operators. Comm. Math. Phys., 132 (1990), 5-25.
    • (1990) Comm. Math. Phys. , vol.132 , pp. 5-25
    • Fröhlich, J.1    Spencer, T.2    Wittwer, P.3
  • 15
    • 0040517213 scopus 로고    scopus 로고
    • The xi function
    • GESZTESY, F. & SIMON, B., The xi function. Acta Math., 176 (1996), 49-71.
    • (1996) Acta Math. , vol.176 , pp. 49-71
    • Gesztesy, F.1    Simon, B.2
  • 17
    • 0002330387 scopus 로고
    • Semi-classical analysis for Harper's equation, III. Cantor structure of the spectrum
    • HELFFER, B. & SJÖSTRAND, J., Semi-classical analysis for Harper's equation, III. Cantor structure of the spectrum. Mém. Soc. Math. France (N.S.), 39 (1989), 1-139.
    • (1989) Mém. Soc. Math. France (N.S.) , vol.39 , pp. 1-139
    • Helffer, B.1    Sjöstrand, J.2
  • 18
    • 21844515681 scopus 로고
    • Anderson localization for the almost Mathieu equation: A nonperturbative proof
    • JITOMIRSKAYA, S., Anderson localization for the almost Mathieu equation: A nonperturbative proof. Comm. Math. Phys., 165 (1994), 49-57.
    • (1994) Comm. Math. Phys. , vol.165 , pp. 49-57
    • Jitomirskaya, S.1
  • 19
    • 0001885983 scopus 로고
    • Almost everything about the almost Mathieu operator, II
    • Internat. Press, Cambridge, MA
    • _ Almost everything about the almost Mathieu operator, II, in XIth International Congress of Mathematical Physics (Paris, 1994), pp. 373-382. Internat. Press, Cambridge, MA, 1995.
    • (1994) XIth International Congress of Mathematical Physics (Paris) , pp. 373-382
  • 20
    • 21844505868 scopus 로고
    • Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators
    • JITOMIRSKAYA, S. & SIMON, B., Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators. Comm. Math. Phys., 165 (1994), 201-205.
    • (1994) Comm. Math. Phys. , vol.165 , pp. 201-205
    • Jitomirskaya, S.1    Simon, B.2
  • 21
    • 33846873343 scopus 로고
    • A relation between a.c. spectrum of ergodic Jacobi matrices arid the spectra of periodic approximants
    • LAST, Y., A relation between a.c. spectrum of ergodic Jacobi matrices arid the spectra of periodic approximants. Comm. Math. Phys., 151 (1993), 183-192.
    • (1993) Comm. Math. Phys. , vol.151 , pp. 183-192
    • Last, Y.1
  • 22
    • 33847667155 scopus 로고
    • Zero measure for the almost Mathieu operator
    • _ Zero measure for the almost Mathieu operator. Comm. Math. Phys., 164 (1994), 421-432.
    • (1994) Comm. Math. Phys. , vol.164 , pp. 421-432
  • 23
    • 0001885983 scopus 로고
    • Almost everything about the almost Mathieu operator, I
    • Internat. Press, Cambridge, MA
    • _ Almost everything about the almost Mathieu operator, I, in XIth International Congress of Mathematical Physics (Paris, 1994), pp. 366-372. Internat. Press, Cambridge, MA, 1995.
    • (1994) XIth International Congress of Mathematical Physics (Paris) , pp. 366-372
  • 25
    • 0009143996 scopus 로고
    • 1D-quasiperiodic operators. Latent symmetries
    • MANDELSHTAM, V. & ZHITOMIRSKAYA, S.. 1D-quasiperiodic operators. Latent symmetries. Comm. Math. Phys., 139 (1991), 589-604.
    • (1991) Comm. Math. Phys. , vol.139 , pp. 589-604
    • Mandelshtam, V.1    Zhitomirskaya, S.2
  • 26
    • 0001758451 scopus 로고
    • Spectral analysis of rank one perturbations and applications
    • CRM Proc. Lecture Notes, 8. Amer. Math. Soc., Providence, RI
    • SIMON, B., Spectral analysis of rank one perturbations and applications, in Mathematical Quantum Theory, II. Schrödinger Operators (Vancouver, BC, 1993), pp. 109-149. CRM Proc. Lecture Notes, 8. Amer. Math. Soc., Providence, RI, 1995.
    • (1993) Mathematical Quantum Theory, II. Schrödinger Operators (Vancouver, BC) , vol.2 , pp. 109-149
    • Simon, B.1
  • 27
    • 0000763917 scopus 로고
    • Anderson localization for one-dimensional Schrödinger operator with quasiperiodic potential
    • SINAI, YA., Anderson localization for one-dimensional Schrödinger operator with quasiperiodic potential. J. Statist. Phys., 46 (1987), 861-909.
    • (1987) J. Statist. Phys. , vol.46 , pp. 861-909
    • Sinai, Ya.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.