Preview
Unable to display preview. Download preview PDF.
References
T.Kato:Integration of the equation of evolution in Banach space, J. Math. Soc. Japan 5(1953), 208–234.
T.Kato: On linear differential equations in Banach spaces, Comm. Pure Appl. Math. 9 (1956) 479–486.
T.Kato: Abstract evolution equation of parabolic type in Banach and Hilbert spaces, Nagoya Math. J. 19 (1961),93–125.
T.Kato, H.Tanabe: On the abstract evolution equation, Osaka Math. J. 14 (1962), 107–133.
T.Kato: Linear evolution equations of “hyperbolic” type, J. Fac. Science, University of Tokyo, Sect. IA, Mathematics, 17 (1970), 241–258.
T.Kato: Linear evolution equations of “hyperbolic” type, II, J. Math. Soc. Japan 25 (1973), 648–666.
M.Reed, B.Simon:“Methods of Modern Mathematical Physics I: Fourier Analysis, Selfadjointness”, Academic Press, New-York-San Francisco-London 1975.
K.Yajima: Existence of solutions for Schrödinger evolution equations, Comm. Math. Physics 110 (1987), 415–426.
H.Neidhardt: “Integration von Evolutionsgleichungen mit Hilfe von Evolutionshalbgruppen”, Dissertation, AdW der DDR, Berlin 1979.
H.Neidhardt: On abstract linear evolution equations, II, Preprint, AdW der DDR, Institut für Mathematik, P-MATH-07/81, Berlin 1981.
O.A.Ladyženskaja: On the solution of operator equations of different types, Doklady Akad. Nauk SSSR 102 (1955), 207–210 (in Russian).
O.A.Ladyzenskaja: On the solution of non-stationary operator equations, Mat. Sbornik 39 (1956), 491–524(in Russian).
J.L.Lions: Equations différentielles á coefficients opérateurs non bornés, Bull. Soc. Math. France 86 (1958), 321–330.
J.L.Lions: Sur certaines equations aux derivees partielles a coefficients operateurs non bornés, J. Anal. Math. 6 (1958), 333–355.
J.L.Lions: Equations différentielles du premier ordre dans un espace de Hilbert, C.R. Acad. Sci. Paris, série A, 248 (1959), 1099–1102.
G.DaPrato: Weak solutions for linear abstract differential equations in Banach spaces, Advances in Mathematics 5 (1970), 181–245.
G.DaPrato: Sums of linear operators, in: “Linear Operators and Approximation, II”, Proceedings of the Conference held at the Oberwolfach Mathematical Research Institute, Black Forest, March 30–April 6, 1974, pp. 461-472 (eds. P.L.Butzer, B.Sz.-Nagy).
M.Iannelli: On the Green function for abstract evolution equations, Bolletino U.M.I. (4) 6 (1972), 154–174.
G.DaPrato, P.Grisvard: Sommes d'opérateurs linéaires et équations différentielles opérationelles, J. Math. Pures Appliquées 54 (1975), 305–387.
L.Paquet: Equations d'evolution pour opérateurs locaux et équations aux derivées partielles, C.R. Acad. Sci. Paris, serie A, 284(1977).
J.S.Howland: Stationary scattering theory for time-dependent hamiltonians, Math. Ann. 207 (1974)-. 315–335.
H.Neidhardt: On abstract linear evolution equations. I. Math. Nachr. 103 (1981), 283–298.
H.Neidhardt: On abstract linear evolution equations. III. Preprint. AdW der DDR, Institut für Mathematik, P-MATH-05/82, Berlin 1982.
M.Reed, B.Simon:“Methods of Modern Mathematical Physics I: Functional Analysis”. Academic Press. New-York-San Francisco-London 1974.
B.Fuglede: On the relation PQ-QP = −iI. Math. Scand. 20 (1967), 79–88.
N.S.Poulsen: On the canonical commutation relations. Math. Scand. 32 (1973), 112–122.
P.E.T.Jørgensen: Selfadjoint operator extensions satisfying the Weyl commutation relations, Bull. (New Series) Amer. Math. Soc. 1 (1979), 1, 266–269.
P.E.T.Jørgensen, P.S.Muhly: Self-adjoint extensions satisfying the Weyl operator commutation relations. J. d'Analyse Math. 37 (1980), 46–99.
W.J.Phillips: On the relation PQ-QP = −iI. Pac. J. Math. 95 (1981), 435–441.
K.Schmüdgen: On the Heisenberg commutation relation I. J. Funct. Analysis 50 (1983), 8–49.
K.Schmüdgen: On the Heisenberg commutation relation II. Publ. RIMS. Kyoto Univ. 19 (1983), 601–671.
G.Dorfmeister, J.Dorfmeister: Classification of certain pairs of operators (P,Q) satisfying [P,Q] = −iId, J. Funct. Analysis 57 (1984), 301–328.
H.Neidhardt: Symmetric extensions preserving additional conditions, Preprint, AdW der DDR, Institut für Mathematik, P-MATH-16/82, Berlin 1982.
N.I.Achieser, I.M.Glasmann: “Theorie der linearen Operatoren im Hilbert-Raum”, Akademie-Verlag, Berlin 1975.
J.Bognar: “Indefinite inner product spaces”, Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 78, Springer Verlag, Berlin-Heidelberg-New York 1974.
T.Ja.Azizov, I.S.Jodvidov: “Basics facts about linear operators in spaces with indefinite metric”, Izd. “Nauka”, Moskva 1986 (in Russian).
M.A.Naimark, R.S.Ismagilov: Representation of groups and algebras with indefinite metric, Itogi nauki, mat. anal. 1968, AN SSSR, Institute Sci. Information, Moskva 1969.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Neidhardt, H. (1989). Evolution equations and selfadjoint extensions. In: Exner, P., Šeba, P. (eds) Applications of Self-Adjoint Extensions in Quantum Physics. Lecture Notes in Physics, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022954
Download citation
DOI: https://doi.org/10.1007/BFb0022954
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50883-0
Online ISBN: 978-3-540-46104-3
eBook Packages: Springer Book Archive