메뉴 건너뛰기




Volumn 8, Issue 3, 2008, Pages 291-301

Convergence of the magnus series

Author keywords

Baker Campbell Hausdorff formula; Exponential Lie series; Linear ordinary differential equations; Magnus series

Indexed keywords

BAKER-CAMPBELL-HAUSDORFF FORMULA; FUNDAMENTAL SOLUTIONS; INFINITE SERIES; LIE SERIES; LINEAR ORDINARY DIFFERENTIAL EQUATIONS; MAGNUS SERIES; MATRIX EXPONENTIALS;

EID: 45849094448     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-007-9010-0     Document Type: Article
Times cited : (101)

References (23)
  • 1
    • 0000081791 scopus 로고
    • Chronological algebras and nonstationary vector fields
    • A. Agračhev and R. Gamkrelidze, Chronological algebras and nonstationary vector fields, J. Sov. Math. 17 (1981), 1650-1675.
    • (1981) J. Sov. Math. , vol.17 , pp. 1650-1675
    • Agračhev, A.1    Gamkrelidze, R.2
  • 2
    • 0039286108 scopus 로고
    • Explicit solution of the continuous Baker-Campbell-Hausdorff problem and a new expression for the phase operator
    • I. Bialynicki-Birula, B. Mielnik, and J. Plebański, Explicit solution of the continuous Baker-Campbell-Hausdorff problem and a new expression for the phase operator, Ann. Phys. 51 (1969), 187-200.
    • (1969) Ann. Phys. , vol.51 , pp. 187-200
    • Bialynicki-Birula, I.1    Mielnik, B.2    Plebański, J.3
  • 3
    • 0032498043 scopus 로고    scopus 로고
    • Magnus and Fer expansions for matrix differential equations: The convergence problem
    • S. Blanes, F. Casas, J. Oteo, and J. Ros, Magnus and Fer expansions for matrix differential equations: The convergence problem, J. Phys. A 31 (1998), 259-268.
    • (1998) J. Phys. A , vol.31 , pp. 259-268
    • Blanes, S.1    Casas, F.2    Oteo, J.3    Ros, J.4
  • 4
    • 0000819022 scopus 로고
    • Recursion formulas for the Lie integral
    • R. V. Chacon and A. T. Fomenko, Recursion formulas for the Lie integral, Adv. Math. 88 (1991), 200-257.
    • (1991) Adv. Math. , vol.88 , pp. 200-257
    • Chacon, R.V.1    Fomenko, A.T.2
  • 5
    • 0039892431 scopus 로고
    • Convergence of the Magnus expansion
    • 5
    • F. M. Fernández, Convergence of the Magnus expansion, Phys. Rev. A 41(5) (1990), 2311-2314.
    • (1990) Phys. Rev. A , vol.41 , pp. 2311-2314
    • Fernández, F.M.1
  • 6
    • 0004131235 scopus 로고
    • Chelsea New York Two volumes. Translated by K.A. Hirsch
    • F. R. Gantmacher, The Theory of Matrices, Chelsea, New York, 1959. Two volumes. Translated by K.A. Hirsch.
    • (1959) The Theory of Matrices
    • Gantmacher, F.R.1
  • 8
    • 2542422820 scopus 로고    scopus 로고
    • Expansions that grow on trees
    • 4
    • A. Iserles, Expansions that grow on trees, Not. Am. Math. Soc. 49(4) (2002), 430-440.
    • (2002) Not. Am. Math. Soc. , vol.49 , pp. 430-440
    • Iserles, A.1
  • 9
    • 0346968523 scopus 로고    scopus 로고
    • On the solution of linear differential equations in Lie groups
    • 1754
    • A. Iserles and S. Nørsett, On the solution of linear differential equations in Lie groups, Philos. Trans. R. Soc. Lond. Ser. A 357(1754) (1999), 983-1019.
    • (1999) Philos. Trans. R. Soc. Lond. Ser. A , vol.357 , pp. 983-1019
    • Iserles, A.1    Nørsett, S.2
  • 10
    • 0346516514 scopus 로고
    • Infinite products and T-products of exponents
    • 2
    • M. V. Karasëv and M. V. Mosolova, Infinite products and T-products of exponents, Theor. Math. Phys. 28(2) (1977), 721-729.
    • (1977) Theor. Math. Phys. , vol.28 , pp. 721-729
    • Karasëv, M.V.1    Mosolova, M.V.2
  • 11
    • 0041079459 scopus 로고
    • The Baker-Campbell-Hausdorff formula and the convergence of the Magnus expansion
    • 21
    • S. Klarsfeld and J. A. Oteo, The Baker-Campbell-Hausdorff formula and the convergence of the Magnus expansion, J. Phys. A 22(21) (1989), 4565-4572.
    • (1989) J. Phys. A , vol.22 , pp. 4565-4572
    • Klarsfeld, S.1    Oteo, J.A.2
  • 12
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear operator
    • W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7 (1954), 639-673.
    • (1954) Commun. Pure Appl. Math. , vol.7 , pp. 639-673
    • Magnus, W.1
  • 15
    • 0035578990 scopus 로고    scopus 로고
    • Convergence of the exponential Lie series
    • 1
    • P. C. Moan and J. A. Oteo, Convergence of the exponential Lie series, J. Math. Phys. 42(1) (2001), 501-507.
    • (2001) J. Math. Phys. , vol.42 , pp. 501-507
    • Moan, P.C.1    Oteo, J.A.2
  • 16
    • 0347326195 scopus 로고
    • Convergence domains for the Campbell-Baker-Hausdorff formula
    • 4
    • M. Newman, W. So, and R. C. Thompson, Convergence domains for the Campbell-Baker-Hausdorff formula, Linear Multilinear Algebra 24(4) (1989), 301-310.
    • (1989) Linear Multilinear Algebra , vol.24 , pp. 301-310
    • Newman, M.1    So, W.2    Thompson, R.C.3
  • 17
    • 36849102028 scopus 로고
    • On the exponential form of the time-displacement operator in quantum mechanics
    • P. Pechukas and J. C. Light, On the exponential form of the time-displacement operator in quantum mechanics, J. Chem. Phys. 7 (1966), 3897-3912.
    • (1966) J. Chem. Phys. , vol.7 , pp. 3897-3912
    • Pechukas, P.1    Light, J.C.2
  • 18
    • 0039300308 scopus 로고
    • New criterion for convergence of exponential perturbation theory in the Schrödinger representation
    • 10
    • W. R. Salzman, New criterion for convergence of exponential perturbation theory in the Schrödinger representation, Phys. Rev. A 36(10) (1987), 5074-5076.
    • (1987) Phys. Rev. A , vol.36 , pp. 5074-5076
    • Salzman, W.R.1
  • 19
    • 0000636861 scopus 로고
    • The Campbell-Baker-Hausdorff-Dynkin formula and solution of differential equations
    • R. S. Strichartz, The Campbell-Baker-Hausdorff-Dynkin formula and solution of differential equations, J. Funct. Anal. 72 (1987), 320-345.
    • (1987) J. Funct. Anal. , vol.72 , pp. 320-345
    • Strichartz, R.S.1
  • 20
    • 5544238546 scopus 로고
    • On the convergence of exponential operators-the Zassenhaus formula, BCH formula and systematic approximants
    • 3
    • M. Suzuki, On the convergence of exponential operators-the Zassenhaus formula, BCH formula and systematic approximants, Commun. Math. Phys. 57(3) (1977), 193-200.
    • (1977) Commun. Math. Phys. , vol.57 , pp. 193-200
    • Suzuki, M.1
  • 23
    • 27144540689 scopus 로고    scopus 로고
    • Explicit solution of a linear ordinary differential equation and a basic property of the exponential function
    • 3
    • V. A. Vinokurov, Explicit solution of a linear ordinary differential equation and a basic property of the exponential function, Diff. Equ. 33(3) (1997), 298-304.
    • (1997) Diff. Equ. , vol.33 , pp. 298-304
    • Vinokurov, V.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.