메뉴 건너뛰기




Volumn 152, Issue 2, 2000, Pages 593-643

A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure

Author keywords

Inverse spectral theory; Spectral measure; Weyl Titchmarsh m function

Indexed keywords


EID: 0034257480     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2661393     Document Type: Article
Times cited : (103)

References (39)
  • 3
    • 84971134623 scopus 로고
    • On the location of the Weyl circles
    • F. V. ATKINSON, On the location of the Weyl circles, Proc. Roy. Soc. Edinburgh 88A (1981), 345-356.
    • (1981) Proc. Roy. Soc. Edinburgh , vol.88 A , pp. 345-356
    • Atkinson, F.V.1
  • 4
    • 0000672810 scopus 로고
    • Spectral asymptotics for Sturm-Liouville equations
    • C. BENNEWITZ, Spectral asymptotics for Sturm-Liouville equations, Proc. London Math. Soc. 59 (1989), 294-338.
    • (1989) Proc. London Math. Soc. , vol.59 , pp. 294-338
    • Bennewitz, C.1
  • 7
    • 0001590635 scopus 로고
    • On the asymptotic behavior of the Weyl-Titchmarsh m-function
    • A. A. DANIELYAN and B. M. LEVITAN, On the asymptotic behavior of the Weyl-Titchmarsh m-function, Math. USSR Izv. 36 (1991), 487-496.
    • (1991) Math. USSR Izv. , vol.36 , pp. 487-496
    • Danielyan, A.A.1    Levitan, B.M.2
  • 9
    • 0002054433 scopus 로고    scopus 로고
    • private communication
    • R. DEL RIO, private communication.
    • Del Rio, R.1
  • 10
    • 84959808377 scopus 로고
    • On a property of the m-coefficient of a second-order linear differential equation
    • W. N. EVERITT, On a property of the m-coefficient of a second-order linear differential equation, J. London Math. Soc. 4 (1972), 443-457.
    • (1972) J. London Math. Soc. , vol.4 , pp. 443-457
    • Everitt, W.N.1
  • 11
    • 33845774185 scopus 로고
    • The inverse problem in the quantum theory of scattering
    • L. D. FADDEEV, The inverse problem in the quantum theory of scattering, J. Mathematical Phys. 4 (1963), 72-104.
    • (1963) J. Mathematical Phys. , vol.4 , pp. 72-104
    • Faddeev, L.D.1
  • 12
    • 0001458591 scopus 로고
    • On the determination of a differential equation from its special function
    • Russian
    • I. M. GEL'FAND and B. M. LEVITAN, On the determination of a differential equation from its special function, Izv. Akad. Nauk SSSR. Ser. Mat. 15 (1951), 309-360 (Russian); English transl. in Amer. Math. Soc. Transl. 1 (1955), 253-304.
    • (1951) Izv. Akad. Nauk SSSR. Ser. Mat. , vol.15 , pp. 309-360
    • Gel'fand, I.M.1    Levitan, B.M.2
  • 13
    • 0001649889 scopus 로고
    • I. M. GEL'FAND and B. M. LEVITAN, On the determination of a differential equation from its special function, Izv. Akad. Nauk SSSR. Ser. Mat. 15 (1951), 309-360 (Russian); English transl. in Amer. Math. Soc. Transl. 1 (1955), 253-304.
    • (1955) Amer. Math. Soc. Transl. , vol.1 , pp. 253-304
  • 15
    • 0002165426 scopus 로고
    • On the high-energy behaviour of scattering phase shifts for Coulomb-like potentials
    • F. GESZTESY, W. PLESSAS, and B. THALLER, On the high-energy behaviour of scattering phase shifts for Coulomb-like potentials, J. Phys. A 13 (1980), 2659-2671.
    • (1980) J. Phys. A , vol.13 , pp. 2659-2671
    • Gesztesy, F.1    Plessas, W.2    Thaller, B.3
  • 17
    • 2442538383 scopus 로고    scopus 로고
    • The form of the spectral functions associated with Sturm-Liouville problems with continuous spectrum
    • B. J. HARRIS, The form of the spectral functions associated with Sturm-Liouville problems with continuous spectrum, Mathematika 44 (1997), 149-161.
    • (1997) Mathematika , vol.44 , pp. 149-161
    • Harris, B.J.1
  • 18
    • 84972506410 scopus 로고
    • Series representation and asymptotics for Titchmarsh-Weyl m-functions
    • D. B. HINTON, M. KLAUS, and J. K. SHAW, Series representation and asymptotics for Titchmarsh-Weyl m-functions, Differential Integral Equations 2 (1989), 419-429.
    • (1989) Differential Integral Equations , vol.2 , pp. 419-429
    • Hinton, D.B.1    Klaus, M.2    Shaw, J.K.3
  • 19
    • 0000877412 scopus 로고
    • On the asymptotic behavior of the spectral function of a self-adjoint second order differential equation
    • B. M. LEVITAN, On the asymptotic behavior of the spectral function of a self-adjoint second order differential equation, Amer. Math. Soc. Transl. 101 (1973), 192-221.
    • (1973) Amer. Math. Soc. Transl. , vol.101 , pp. 192-221
    • Levitan, B.M.1
  • 20
    • 0002036319 scopus 로고
    • On the asymptotic behavior of the spectral function of a self-adjoint differential equation of the second order and on expansion in eigenfunctions
    • _, On the asymptotic behavior of the spectral function of a self-adjoint differential equation of the second order and on expansion in eigenfunctions, Amer. Math. Soc. Transl. 102 (1973), 191-229.
    • (1973) Amer. Math. Soc. Transl. , vol.102 , pp. 191-229
  • 21
    • 0002039756 scopus 로고
    • On the asymptotic behavior of the spectral function of a self-adjoint differential equation of the second order and on expansion in eigenfunctions. II
    • _, On the asymptotic behavior of the spectral function of a self-adjoint differential equation of the second order and on expansion in eigenfunctions. II, Amer. Math. Soc. Transi. 110 (1977), 165-188.
    • (1977) Amer. Math. Soc. Transi. , vol.110 , pp. 165-188
  • 23
    • 0001116357 scopus 로고
    • Determination of a differential equation by two of its spectra
    • B. M. LEVITAN and M. G. GASYMOV, Determination of a differential equation by two of its spectra, Russian Math. Surveys 19:2 (1964), 1-63.
    • (1964) Russian Math. Surveys , vol.19 , Issue.2 , pp. 1-63
    • Levitan, B.M.1    Gasymov, M.G.2
  • 25
    • 0002310536 scopus 로고
    • Similarity of Volterra operators and related problems in the theory of differential equations of fractional order
    • M. M. MALAMUD, Similarity of Volterra operators and related problems in the theory of differential equations of fractional order, Trans. Moscow Math. Soc. 55 (1994), 57-122.
    • (1994) Trans. Moscow Math. Soc. , vol.55 , pp. 57-122
    • Malamud, M.M.1
  • 26
    • 0002313175 scopus 로고    scopus 로고
    • Uniqueness questions in inverse problems for systems of ordinary differential equations on a finite interval
    • Russian
    • _, Uniqueness questions in inverse problems for systems of ordinary differential equations on a finite interval, Trans. Moscow Math. Soc. 60 (1998), 204-263 (Russian).
    • (1998) Trans. Moscow Math. Soc. , vol.60 , pp. 204-263
  • 27
    • 0001859367 scopus 로고
    • Some questions in the theory of one-dimensional linear differential operators of the second order. I
    • V. A. MARCENKO, Some questions in the theory of one-dimensional linear differential operators of the second order. I, Amer. Math. Soc. Transl. 101 (1973), 1-104.
    • (1973) Amer. Math. Soc. Transl. , vol.101 , pp. 1-104
    • Marcenko, V.A.1
  • 28
    • 0000106135 scopus 로고
    • Theorems of Tauberian type in the spectral analysis of differential operators
    • _, Theorems of Tauberian type in the spectral analysis of differential operators, Amer. Math. Soc. Transl. 102 (1973), 145-190.
    • (1973) Amer. Math. Soc. Transl. , vol.102 , pp. 145-190
  • 30
    • 0001608151 scopus 로고
    • Operator methods for inverse scattering on the real line
    • A. MELIN, Operator methods for inverse scattering on the real line, Comm. Partial Differential Equations 10 (1985), 677-766.
    • (1985) Comm. Partial Differential Equations , vol.10 , pp. 677-766
    • Melin, A.1
  • 32
    • 0002320249 scopus 로고
    • Recovery of the potential from the I-function
    • A. G. RAMM, Recovery of the potential from the I-function, C. R. Math. Rep. Acad. Sci. Canada IX (1987), 177-182.
    • (1987) C. R. Math. Rep. Acad. Sci. Canada , vol.9 , pp. 177-182
    • Ramm, A.G.1
  • 36
    • 0033235955 scopus 로고    scopus 로고
    • A new approach to inverse spectral theory, I. Fundamental formalism
    • _, A new approach to inverse spectral theory, I. Fundamental formalism, Ann. of Math. 150 (1999), 1029-1057.
    • (1999) Ann. of Math. , vol.150 , pp. 1029-1057
  • 37
    • 0018531924 scopus 로고
    • Inverse boundary value problems and a theorem of Gel'fand and Levitan
    • W. SYMES, Inverse boundary value problems and a theorem of Gel'fand and Levitan, J. Math. Anal. Appl. 71 (1979), 379-402.
    • (1979) J. Math. Anal. Appl. , vol.71 , pp. 379-402
    • Symes, W.1
  • 38
    • 84976137631 scopus 로고
    • A generalisation of the inverse spectral theorem of Levitan and Gasymov
    • C. THURLOW, A generalisation of the inverse spectral theorem of Levitan and Gasymov, Proc. Roy. Soc. Edinburgh 84A (1979), 185-196.
    • (1979) Proc. Roy. Soc. Edinburgh , vol.84 A , pp. 185-196
    • Thurlow, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.