메뉴 건너뛰기




Volumn 142, Issue 2, 2007, Pages 365-384

A star-graph model via operator extension

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34247885914     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/S0305004106009820     Document Type: Article
Times cited : (15)

References (48)
  • 1
    • 34247856489 scopus 로고    scopus 로고
    • J. VON NEUMANN. Mathematical Foundations of Quantum Mechanics (Twelfth printing. Princeton Landmarks in Mathematics. Princeton Paperbacks. (Princeton University Press, 1996).
    • J. VON NEUMANN. Mathematical Foundations of Quantum Mechanics (Twelfth printing. Princeton Landmarks in Mathematics. Princeton Paperbacks. (Princeton University Press, 1996).
  • 2
    • 0000447975 scopus 로고
    • A remark on Schrödinger equation with a singular potential
    • F. A.BEREZIN and L. D. FADDEEV. A remark on Schrödinger equation with a singular potential. Doklady AN SSSR 137 (1961), 1011-1014.
    • (1961) Doklady AN SSSR , vol.137 , pp. 1011-1014
    • BEREZIN, F.A.1    FADDEEV, L.D.2
  • 5
    • 0003300938 scopus 로고    scopus 로고
    • Singular Perturbations of Differential Operators
    • London Math, Cambridge University Press
    • S. ALBEVERIO and P. KURASOV. Singular Perturbations of Differential Operators. London Math. Society Lecture Note Series 271 (Cambridge University Press, 2000).
    • (2000) Society Lecture Note Series , vol.271
    • ALBEVERIO, S.1    KURASOV, P.2
  • 6
    • 3343011966 scopus 로고    scopus 로고
    • Adjoint and self-adjoint differential operators on graphs
    • R. CARLSON, Adjoint and self-adjoint differential operators on graphs. Electronic J. Diff. Eq. 6 (1998), 10.
    • (1998) Electronic J. Diff. Eq , vol.6 , pp. 10
    • CARLSON, R.1
  • 8
    • 34247886574 scopus 로고    scopus 로고
    • S. P. NOVIKOV. Schrodinger operators on graphs and symplectic geometry. The Arnoldfest (Toronto, ON, 1997). Fields Inst. Commun. 24 (1999), 397-413.
    • S. P. NOVIKOV. Schrodinger operators on graphs and symplectic geometry. The Arnoldfest (Toronto, ON, 1997). Fields Inst. Commun. 24 (1999), 397-413.
  • 9
  • 11
    • 0035877564 scopus 로고    scopus 로고
    • Convergence of spectra of mesoscopic systems collapsing onto graph
    • P. KUCHMENT and H. ZENG. Convergence of spectra of mesoscopic systems collapsing onto graph J. Math. Anal. Appl. 258 (2001), 671-700.
    • (2001) J. Math. Anal. Appl , vol.258 , pp. 671-700
    • KUCHMENT, P.1    ZENG, H.2
  • 12
    • 34247879338 scopus 로고    scopus 로고
    • V. BOGEVOLNOV, A, MIKHAILOVA, B. PAVLOV and A. YAFYASOV. About scattering on the ring. In: 'Oper. Theory' Adv. Appl. 124 (Israel Gohberg Anniversary Ed. A. Dijksma, A. M. Kaashoek, A. C. M. Ran. (2001), 155-187.
    • V. BOGEVOLNOV, A, MIKHAILOVA, B. PAVLOV and A. YAFYASOV. About scattering on the ring. In: 'Oper. Theory' Adv. Appl. 124 (Israel Gohberg Anniversary Volume), Ed. A. Dijksma, A. M. Kaashoek, A. C. M. Ran. (2001), 155-187.
  • 13
    • 0036070133 scopus 로고    scopus 로고
    • Scattering on compact domain with few semi-infinite wires attached: Resonance case
    • A. MIKHAILOVA, B. PAVLOV, I. POPOV, T. RUDAKOVA and A. YAFYASOV. Scattering on compact domain with few semi-infinite wires attached: resonance case. Math. Nachri 235, 1 (2002), 102-128.
    • (2002) Math. Nachri , vol.235 , Issue.1 , pp. 102-128
    • MIKHAILOVA, A.1    PAVLOV, B.2    POPOV, I.3    RUDAKOVA, T.4    YAFYASOV, A.5
  • 15
    • 11144357427 scopus 로고    scopus 로고
    • Spectral properties of a short-range impurity in a quantum dot
    • J. BRÜNING, V. GEYLER and I. LOBANOV. Spectral properties of a short-range impurity in a quantum dot. J. Math. Phys. 45, 4 (2004), 1267-1290.
    • (2004) J. Math. Phys , vol.45 , Issue.4 , pp. 1267-1290
    • BRÜNING, J.1    GEYLER, V.2    LOBANOV, I.3
  • 16
    • 0942278569 scopus 로고    scopus 로고
    • On the spectrum of Laplacian on regular metric trees
    • M. Z. SOLOMYAK. On the spectrum of Laplacian on regular metric trees. Waves Random Media 14, 1 (2004) 155-171.
    • (2004) Waves Random Media , vol.14 , Issue.1 , pp. 155-171
    • SOLOMYAK, M.Z.1
  • 17
    • 0035624180 scopus 로고    scopus 로고
    • Variational approach on multiply connected thin strips I: Basic estimates and convergence of the Laplacian spectrum
    • J. RUBINSHTEIN and M. SHATZMAN. Variational approach on multiply connected thin strips I: Basic estimates and convergence of the Laplacian spectrum. Arch. Ration. Mech. Analysis 160, 4 (2001), 271-308.
    • (2001) Arch. Ration. Mech. Analysis , vol.160 , Issue.4 , pp. 271-308
    • RUBINSHTEIN, J.1    SHATZMAN, M.2
  • 18
    • 0011159356 scopus 로고    scopus 로고
    • Convergence of the Neumann Laplacian on shrinking domains
    • Y. SAITO. Convergence of the Neumann Laplacian on shrinking domains. Analysis 21 (2001), 171-204.
    • (2001) Analysis , vol.21 , pp. 171-204
    • SAITO, Y.1
  • 19
    • 0008597896 scopus 로고
    • Reaction-diffusion equations with randomly perturbed boundary conditions
    • A. WENTZEL and M. FREIDLIN. Reaction-diffusion equations with randomly perturbed boundary conditions. Ann. Probab. 20, 2 (1992), 963-986.
    • (1992) Ann. Probab , vol.20 , Issue.2 , pp. 963-986
    • WENTZEL, A.1    FREIDLIN, M.2
  • 20
    • 84975712426 scopus 로고    scopus 로고
    • On the eigenvalues of the Laplace operator on a thin set with Neumann boundary conditions
    • M. SHATZMAN. On the eigenvalues of the Laplace operator on a thin set with Neumann boundary conditions. Appl. Anal. 61 (1996), 293 - 306.
    • (1996) Appl. Anal , vol.61 , pp. 293-306
    • SHATZMAN, M.1
  • 21
    • 16244421065 scopus 로고    scopus 로고
    • Convergence of spectra of graph-like thin manifolds
    • P. EXNER and O. POST. Convergence of spectra of graph-like thin manifolds. J. Geom. Phys. 54, 1 (2005), 77-115.
    • (2005) J. Geom. Phys , vol.54 , Issue.1 , pp. 77-115
    • EXNER, P.1    POST, O.2
  • 22
    • 0242307817 scopus 로고    scopus 로고
    • Value disttribution of the eigenfunctions and spectral determinants of quantum star-graphs
    • J. P. KEATING, J. MARLOF and B. WINN. Value disttribution of the eigenfunctions and spectral determinants of quantum star-graphs. Commun. Math. Phys. 241, 2-3 (2003), 421- 452.
    • (2003) Commun. Math. Phys , vol.241 , Issue.2-3 , pp. 421-452
    • KEATING, J.P.1    MARLOF, J.2    WINN, B.3
  • 23
    • 5644248409 scopus 로고    scopus 로고
    • No quantum ergodicity for star graphs
    • J. P. Keating, B. Winn. No quantum ergodicity for star graphs. Commun. Math. Phys. 250, 2 (2004), 219-285.
    • (2004) Commun. Math. Phys , vol.250 , Issue.2 , pp. 219-285
    • Keating, J.P.1    Winn, B.2
  • 24
    • 34247843517 scopus 로고    scopus 로고
    • J. SYLVESTER and G. UHLMANN. The Dirichlet to Neumann map and applications. In: Proceedings of the Conference. 'Inverse problems in partial differential equations (Arcata, 1989)', SIAM ( 1990), 101-139.
    • J. SYLVESTER and G. UHLMANN. The Dirichlet to Neumann map and applications. In: Proceedings of the Conference. 'Inverse problems in partial differential equations (Arcata, 1989)', SIAM ( 1990), 101-139.
  • 25
    • 34247880954 scopus 로고    scopus 로고
    • B. PAVLOV, S-Matrix and Dirichlet-to-Neumann Operators. In: Scattering (Encyclopedia of Scattering), ed. R. Pike, P. Sabatier (Academic Press, Harcourt Science and Tech. Company, Ch 1.6.1 2001), 1678-1688.
    • B. PAVLOV, S-Matrix and Dirichlet-to-Neumann Operators. In: Scattering (Encyclopedia of Scattering), ed. R. Pike, P. Sabatier (Academic Press, Harcourt Science and Tech. Company, Ch 1.6.1 2001), 1678-1688.
  • 26
    • 3042526641 scopus 로고    scopus 로고
    • M-operators: A generalization of Weyl-Titchmarsh theory
    • W. O. AMREIN and D. B. PEARSON, M-operators: a generalization of Weyl-Titchmarsh theory. J. Comp. Appl. Math. 171, 1-2 (2004), 1-26.
    • (2004) J. Comp. Appl. Math , vol.171 , Issue.1-2 , pp. 1-26
    • AMREIN, W.O.1    PEARSON, D.B.2
  • 27
    • 3042626305 scopus 로고    scopus 로고
    • Eigenvalue problems on exterior domains and Dirichlet-to-Neumann map
    • M. MARLETTA. Eigenvalue problems on exterior domains and Dirichlet-to-Neumann map. J. Comp. Appl. Math. 171, 1-2 (2004), 367-391.
    • (2004) J. Comp. Appl. Math , vol.171 , Issue.1-2 , pp. 367-391
    • MARLETTA, M.1
  • 28
    • 1642580772 scopus 로고    scopus 로고
    • Spectral inclusion and spectral exactness for PDEs on exterior domain
    • B. M. BROWN and M. MARLETTA. Spectral inclusion and spectral exactness for PDEs on exterior domain. IMA J. Numer. Anal. 24, 1 (2004), 21-3.
    • (2004) IMA J. Numer. Anal , vol.24 , Issue.1 , pp. 21-23
    • BROWN, B.M.1    MARLETTA, M.2
  • 31
    • 34247890679 scopus 로고    scopus 로고
    • O. MADELUNG Introduction to Solid-State Theory. Translated from German by B. C. Taylor. Springer Series in Solid-State Sciences, 2 (Springer-Verlag, 1978).
    • O. MADELUNG Introduction to Solid-State Theory. Translated from German by B. C. Taylor. Springer Series in Solid-State Sciences, 2 (Springer-Verlag, 1978).
  • 34
    • 34247878324 scopus 로고    scopus 로고
    • I. GLAZMAN. Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators. Translated from the Russian by the IPST staff (Israel Program for Scientific Translations), (Jerusalem, 1965), (Daniel Davey and Co., Inc., 1966).
    • I. GLAZMAN. Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators. Translated from the Russian by the IPST staff (Israel Program for Scientific Translations), (Jerusalem, 1965), (Daniel Davey and Co., Inc., 1966).
  • 36
    • 0141865706 scopus 로고    scopus 로고
    • S. LALL, P. KRYSL and J. MARSDEN. Structure-preserving model reduction for mechanical systems. In: Complexity and nonlinearity in physical systems (Tucson, AZ, 2001), Phys. D 184, 1 - 4 (2003), 304-318.
    • S. LALL, P. KRYSL and J. MARSDEN. Structure-preserving model reduction for mechanical systems. In: Complexity and nonlinearity in physical systems (Tucson, AZ, 2001), Phys. D 184, 1 - 4 (2003), 304-318.
  • 37
    • 0008026613 scopus 로고
    • On selfadjoint extensions of Hermitian operators, (in Russian)
    • M. A. KRASNOSEL'SKIJ. On selfadjoint extensions of Hermitian operators, (in Russian). Ukrainskij Mat. J. 1, 21 (1949), 21-38.
    • (1949) Ukrainskij Mat. J , vol.1 , Issue.21 , pp. 21-38
    • KRASNOSEL'SKIJ, M.A.1
  • 38
    • 0002039451 scopus 로고
    • The theory of extensions and explicitly solvable models (In Russian)
    • B. PAVLOV. The theory of extensions and explicitly solvable models (In Russian). Uspekhi Mat. Nauk 42 (1987), 99-131.
    • (1987) Uspekhi Mat. Nauk , vol.42 , pp. 99-131
    • PAVLOV, B.1
  • 39
    • 0039861674 scopus 로고
    • Strongly singular potentials in three-dimensional quantum mechanics (in Russian)
    • J. SHIROKOV. Strongly singular potentials in three-dimensional quantum mechanics (in Russian). Tear. Mat. Fiz. 42, 1 (1980), 45-49.
    • (1980) Tear. Mat. Fiz , vol.42 , Issue.1 , pp. 45-49
    • SHIROKOV, J.1
  • 40
    • 0001747086 scopus 로고
    • Concerning the resolvents of an Hermitian operator with deficiency index (m,m) (in Russian)
    • M. KREIN. Concerning the resolvents of an Hermitian operator with deficiency index (m,m) (in Russian) Doklady AN USSR 52 (1946), 651-654.
    • (1946) Doklady AN USSR , vol.52 , pp. 651-654
    • KREIN, M.1
  • 42
    • 34247846855 scopus 로고    scopus 로고
    • V. I. GORBACHUK. Boundary problems for differential-operator equations (in Russian). Naukova Dumka (1984).
    • V. I. GORBACHUK. Boundary problems for differential-operator equations (in Russian). Naukova Dumka (1984).
  • 43
    • 19944367295 scopus 로고    scopus 로고
    • Jump-start in analytic perturbation procedure for Friedrichs model
    • B. PAVLOV and I. ANTONIOU. Jump-start in analytic perturbation procedure for Friedrichs model. J. Phys. A: Math. Gen. 38 (2005), 4811-823.
    • (2005) J. Phys. A: Math. Gen , vol.38 , pp. 4811-4823
    • PAVLOV, B.1    ANTONIOU, I.2
  • 44
    • 34247883353 scopus 로고    scopus 로고
    • Fitting Parameters for a Solvable Model of a Quantum Network
    • The University of Auckland, 8 p
    • M. HARMER. Fitting Parameters for a Solvable Model of a Quantum Network. The University of Auckland, Department of Mathematics Report Series 514 (2004), 8 p.
    • (2004) Department of Mathematics Report Series , vol.514
    • HARMER, M.1
  • 45
    • 0040597281 scopus 로고
    • A local test for the existence of wave operators (in Russian)
    • M. BIRMAN. A local test for the existence of wave operators (in Russian). Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 914-942.
    • (1968) Izv. Akad. Nauk SSSR Ser. Mat , vol.32 , pp. 914-942
    • BIRMAN, M.1
  • 47
    • 84980077260 scopus 로고
    • On the perturbation of continuous spectra
    • K. O. FRIEDRICHS. On the perturbation of continuous spectra. Commun. Pure Appl. Math. 1 (1948), 361-406.
    • (1948) Commun. Pure Appl. Math , vol.1 , pp. 361-406
    • FRIEDRICHS, K.O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.