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Volumn 201, Issue , 1999, Pages 117-181

Operator interpretation of resonances arising in spectral problems for 2×2 operator matrices

Author keywords

Operator matrix; Operator pencil; Resonance; Riesz basis; Unphysical sheet

Indexed keywords


EID: 0000407522     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19992010107     Document Type: Article
Times cited : (37)

References (46)
  • 1
    • 0041110200 scopus 로고
    • Non-degenerate unitary couplings of semi-unitary operators
    • Russian
    • ADAMJAN, V.M.: Non-Degenerate Unitary Couplings of Semi-Unitary Operators, Funktsional'nyi Analiz i Ego Prilozheniya 7:4 (1973), 1-16 [Russian]
    • (1973) Funktsional'nyi Analiz I Ego Prilozheniya , vol.7 , Issue.4 , pp. 1-16
    • Adamjan, V.M.1
  • 2
    • 0001648740 scopus 로고
    • Spectral properties of a class of operator-valued functions
    • ADAMJAN, V.M., and LANGER, H.: Spectral Properties of a Class of Operator-Valued Functions, J. Operator Theory 33 (1995), 259-277
    • (1995) J. Operator Theory , vol.33 , pp. 259-277
    • Adamjan, V.M.1    Langer, H.2
  • 3
    • 0002969455 scopus 로고    scopus 로고
    • Spectral components of selfadjoint block operator matrices with unbounded entries
    • ADAMYAN, V., LANGER, H., MENNICKEN, R., and SAURER, J.: Spectral Components of Selfadjoint Block Operator Matrices with Unbounded Entries, Math. Nachr. 178 (1996), 43-80
    • (1996) Math. Nachr. , vol.178 , pp. 43-80
    • Adamyan, V.1    Langer, H.2    Mennicken, R.3    Saurer, J.4
  • 6
    • 0041094105 scopus 로고
    • Spektral'naya Teoria Samosopriazhennyh Operatorov v Gil'bertovom Prostranstve, Izdatel'stvo Leningradskogo
    • Universiteta, Leningrad, Reidel, Dordrecht
    • BIRMAN, M. S., and SOLOMJAK, M. Z.: Spektral'naya Teoria Samosopriazhennyh Operatorov v Gil'bertovom Prostranstve, Izdatel'stvo Leningradskogo Universiteta, Leningrad, 1980 [English translation: Spectral Theory of Selfadjoint Operators in Hubert Space, Reidel, Dordrecht, 1987]
    • (1980) Spectral Theory of Selfadjoint Operators in Hubert Space
    • Birman, M.S.1    Solomjak, M.Z.2
  • 7
    • 0039907048 scopus 로고
    • On relation between quasipotential equation and Schrödinger equation
    • Russian
    • BRAUN, M. A.: On Relation between Quasipotential Equation and Schrödinger Equation, Teor. Mat. Fiz. 72 (1987), 394-402 [Russian]
    • (1987) Teor. Mat. Fiz. , vol.72 , pp. 394-402
    • Braun, M.A.1
  • 8
    • 0002447772 scopus 로고
    • Potential scattering with confined channels
    • DASHEN, R. F., HEALY, J. B., and MUZINICH, I. J.: Potential Scattering with Confined Channels Ann. Phys. 102 (1976), 1-70
    • (1976) Ann. Phys. , vol.102 , pp. 1-70
    • Dashen, R.F.1    Healy, J.B.2    Muzinich, I.J.3
  • 10
    • 84980077260 scopus 로고
    • On the perturbation of continuous spectra
    • FRIEDRICHS, K. O.: On the Perturbation of Continuous Spectra, Comm. Pure Appl. Math 1 (1948), 361-406
    • (1948) Comm. Pure Appl. Math , vol.1 , pp. 361-406
    • Friedrichs, K.O.1
  • 11
    • 0000302907 scopus 로고
    • Relativistic theory of interacting particles
    • GLÖCKLE, W., and MÜLLER, L.: Relativistic Theory of Interacting Particles, Phys. Rev. C 23 (1981), 1183-1195
    • (1981) Phys. Rev. C , vol.23 , pp. 1183-1195
    • Glöckle, W.1    Müller, L.2
  • 14
    • 0016510938 scopus 로고
    • The livsic matrix in perturbation theory
    • HOWLAND, J. S.: The Livsic Matrix in Perturbation Theory, J. Math. Anal. Appl. 50 (1975), 415-437
    • (1975) J. Math. Anal. Appl. , vol.50 , pp. 415-437
    • Howland, J.S.1
  • 15
    • 0001504279 scopus 로고
    • Connection between quark-model Eigenstates and low-energy scattering
    • JAFFE, R. L., and LOW, F. E.: Connection between Quark-Model Eigenstates and Low-Energy Scattering, Phys. Rev. D19 (1979), 2105-2118
    • (1979) Phys. Rev. , vol.D19 , pp. 2105-2118
    • Jaffe, R.L.1    Low, F.E.2
  • 17
    • 0009990009 scopus 로고
    • The method of Okubo's effective operators and relativistic model of nuclear structure
    • KORCHIN, A. YU., and SHEBEKO, A. V.: The Method of Okubo's Effective Operators and Relativistic Model of Nuclear Structure, Phys. At. Nucl. 56 (1993), 1663-1671
    • (1993) Phys. At. Nucl. , vol.56 , pp. 1663-1671
    • Korchin, A.Yu.1    Shebeko, A.V.2
  • 18
    • 0007255616 scopus 로고
    • Algebraic version of the extension theory in quantum problem of few particles with internal structure
    • KUPERIN, YU. A., MAKAROV, K. A., MERKURIEV, S. P., and MOTOVILOV, A. K.: Algebraic Version of the Extension Theory in Quantum Problem of Few Particles with Internal Structure, Sov. J. Nucl. Phys. 48 (1988), 224-231
    • (1988) Sov. J. Nucl. Phys. , vol.48 , pp. 224-231
    • Kuperin, Yu.A.1    Makarov, K.A.2    Merkuriev, S.P.3    Motovilov, A.K.4
  • 20
    • 0004168724 scopus 로고
    • Academic Press
    • LAX, P.D., and PHILLIPS, R. S.: Scattering Theory, Academic Press, 1967; Scattering Theory for Automorphic Functions, Prinston U. P., 1976
    • (1967) Scattering Theory
    • Lax, P.D.1    Phillips, R.S.2
  • 21
  • 23
    • 4243268099 scopus 로고
    • The application of non-selfadjoint operators to scattering theory
    • LIVŠIC, M. S.: The Application of Non-Selfadjoint Operators to Scattering Theory, Soviet Physics JETP 4 (1957), 91-98
    • (1957) Soviet Physics JETP , vol.4 , pp. 91-98
    • Livšic, M.S.1
  • 24
    • 0011542590 scopus 로고
    • Invariant subspaces of clustering operators. I
    • MALYSHEV, V. A., and MINLOS, R. A.: Invariant Subspaces of Clustering Operators. I., J. Stat. Phys. 21 (1979), 231-242; Invariant Subspaces of Clustering Operators. II., Comm. Math. Phys. 82 (1981), 211-226
    • (1979) J. Stat. Phys. , vol.21 , pp. 231-242
    • Malyshev, V.A.1    Minlos, R.A.2
  • 25
    • 0011668801 scopus 로고
    • Invariant subspaces of clustering operators. II
    • MALYSHEV, V. A., and MINLOS, R. A.: Invariant Subspaces of Clustering Operators. I., J. Stat. Phys. 21 (1979), 231-242; Invariant Subspaces of Clustering Operators. II., Comm. Math. Phys. 82 (1981), 211-226
    • (1981) Comm. Math. Phys. , vol.82 , pp. 211-226
  • 26
    • 0002076412 scopus 로고
    • On a basis of root vectors of a dissipative operator
    • Russian
    • MARKUS, A. S.: On a Basis of Root Vectors of a Dissipative Operator, Doklady AN SSSR 132 (1960), 524-527 [Russian]
    • (1960) Doklady AN SSSR , vol.132 , pp. 524-527
    • Markus, A.S.1
  • 27
    • 0011658720 scopus 로고
    • On the basis property for a certain part of the Eigen-vectors and associated vectors of a selfadjoint operator pencil
    • MARKUS, A. S., and MATSAEV, V. I.: On the Basis Property for a Certain Part of the Eigen-vectors and Associated Vectors of a Selfadjoint Operator Pencil, Math. USSR Sb. 61 (1988), 289-307.
    • (1988) Math. USSR Sb. , vol.61 , pp. 289-307
    • Markus, A.S.1    Matsaev, V.I.2
  • 28
    • 0039747064 scopus 로고
    • Formal scattering theory for energy-dependent potentials
    • MCKELLAR, B. H. J., and MCKAY C. M.: Formal Scattering Theory for Energy-Dependent Potentials, Aust. J. Phys. 36 (1983), 607-616
    • (1983) Aust. J. Phys. , vol.36 , pp. 607-616
    • McKellar, B.H.J.1    McKay, C.M.2
  • 29
    • 0000822305 scopus 로고    scopus 로고
    • Spectral decomposition of symmetric operator matrices
    • MENNICKEN, R., and SHKALIKOV, A. A.: Spectral Decomposition of Symmetric Operator Matrices, Math. Nachr. 179 (1996), 259-273
    • (1996) Math. Nachr. , vol.179 , pp. 259-273
    • Mennicken, R.1    Shkalikov, A.A.2
  • 30
    • 21344465304 scopus 로고
    • Elimination of energy from interactions depending on it as a resolvent
    • MOTOVILOV, A. K.: Elimination of Energy from Interactions Depending on It as a Resolvent, Theor. Math. Phys. 104 (1995), 989-1007
    • (1995) Theor. Math. Phys. , vol.104 , pp. 989-1007
    • Motovilov, A.K.1
  • 32
    • 21844485785 scopus 로고
    • Removal of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian
    • MOTOVILOV, A. K.: Removal of the Resolvent-Like Energy Dependence from Interactions and Invariant Subspaces of a Total Hamiltonian, J. Math. Phys. 36 (1995), 6647-6664
    • (1995) J. Math. Phys. , vol.36 , pp. 6647-6664
    • Motovilov, A.K.1
  • 33
    • 0031474638 scopus 로고    scopus 로고
    • Representations for the three-body t-matrix, scattering matrices and resolvent on unphysical energy sheets
    • LANL E-print funct - an/9509003
    • MOTOVILOV, A. K.: Representations for the Three-Body T-Matrix, Scattering Matrices and Resolvent on Unphysical Energy Sheets, Math. Nachr. 187 (1997), 147-210 (LANL E-print funct - an/9509003)
    • (1997) Math. Nachr. , vol.187 , pp. 147-210
    • Motovilov, A.K.1
  • 34
    • 0007255929 scopus 로고
    • The removal of an energy dependence from the interaction in two-body systems
    • MOTOVILOV, A. K.: The Removal of an Energy Dependence from the Interaction in Two-Body Systems, J. Math. Phys. 32 (1991), 3509-3518
    • (1991) J. Math. Phys. , vol.32 , pp. 3509-3518
    • Motovilov, A.K.1
  • 35
    • 0000816675 scopus 로고
    • Diagonalization of Hamiltonian and Tamm-Dancoff equation
    • OKUBO, S.: Diagonalization of Hamiltonian and Tamm-Dancoff Equation, Progr. Theor. Phys. 12 (1954), 603-622
    • (1954) Progr. Theor. Phys. , vol.12 , pp. 603-622
    • Okubo, S.1
  • 36
    • 0001011276 scopus 로고
    • A model of zero-radius potential with internal structure
    • Russian
    • PAVLOV, B. S.: A Model of Zero-Radius Potential with Internal Structure, Teor. Mat. Fiz. 59 (1984), 345-353 [Russian]
    • (1984) Teor. Mat. Fiz. , vol.59 , pp. 345-353
    • Pavlov, B.S.1
  • 37
    • 0001396051 scopus 로고
    • On completeness of a set of resonance states for a system of differential equations
    • Russian
    • PAVLOV, B. S.: On Completeness of a Set of Resonance States for a System of Differential Equations, Doklady AN SSSR 196, 6 (1971), 1272-1275 [Russian]; Factorization of the Scattering Matrix and a Serial Structure of its Roots, Izvestiya AN SSSR, mat. 37 (1973), 217-246 [Russian]
    • (1971) Doklady AN SSSR , vol.196 , Issue.6 , pp. 1272-1275
    • Pavlov, B.S.1
  • 38
    • 0010720317 scopus 로고
    • Factorization of the scattering matrix and a serial structure of its roots
    • Russian
    • PAVLOV, B. S.: On Completeness of a Set of Resonance States for a System of Differential Equations, Doklady AN SSSR 196, 6 (1971), 1272-1275 [Russian]; Factorization of the Scattering Matrix and a Serial Structure of its Roots, Izvestiya AN SSSR, mat. 37 (1973), 217-246 [Russian]
    • (1973) Izvestiya AN SSSR , vol.37 , pp. 217-246
  • 39
    • 0009175862 scopus 로고
    • The translation group and harmonic analysis on a Riemann surface
    • English translation in Leningrad Math. J.
    • PAVLOV, B. S., and FEDOROV, S. I.: The Translation Group and Harmonic Analysis on a Riemann Surface, Algebra i Analiz 1 (1989), 132-169 [English translation in Leningrad Math. J.]
    • (1989) Algebra I Analiz , vol.1 , pp. 132-169
    • Pavlov, B.S.1    Fedorov, S.I.2
  • 40
    • 84956132582 scopus 로고
    • The theory of extensions, and null-range potentials with internal structure
    • PAVLOV, B. S., and SHUSHKOV, A. A.: The Theory of Extensions, and Null-Range Potentials with Internal Structure, Math. USSR Sb. 65 (1990), 147-184
    • (1990) Math. USSR Sb. , vol.65 , pp. 147-184
    • Pavlov, B.S.1    Shushkov, A.A.2
  • 43
    • 0003844067 scopus 로고
    • Academic Press, N. Y.
    • REED, M., and SIMON, B.: Methods of Modern Mathematical Physics, III: Scattering Theory, Academic Press, N. Y., 1979; IV: Analysis of Operators, Academic Press, N. Y., 1978
    • (1978) IV: Analysis of Operators
  • 44
    • 0039154626 scopus 로고
    • The problem of using energy-dependent nucleon-nucleon potentials in nuclear physics
    • SCHMID, E. W.: The Problem of Using Energy-Dependent Nucleon-Nucleon Potentials in Nuclear Physics, Helv. Phys. Acta 60 (1987), 394-397.
    • (1987) Helv. Phys. Acta , vol.60 , pp. 394-397
    • Schmid, E.W.1
  • 45
    • 0038910242 scopus 로고
    • Hadron-Hadron interaction in the compound-bag model
    • Russian
    • SIMONOV, YU. A.: Hadron-Hadron Interaction in the Compound-Bag Model, Yadernaya Fiz. 36 (1982), 722-731 [Russian]
    • (1982) Yadernaya Fiz. , vol.36 , pp. 722-731
    • Simonov, Yu.A.1
  • 46
    • 0011542564 scopus 로고
    • The spectral properties of a certain class of selfadjoint operator functions
    • VIROZUB, A. I., and MATSAEV, V. I.: The Spectral Properties of a Certain Class of Selfadjoint Operator Functions, Funct. Anal. Appl. 8 (1974), 1-9
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 1-9
    • Virozub, A.I.1    Matsaev, V.I.2


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