One-parameter semigroups for linear evolution equations

Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.

[1]  Vito Volterra,et al.  Lecons sur les fonctions de lignes , 1913 .

[2]  M. Stone Linear transformations in Hilbert space and their applications to analysis , 1932 .

[3]  M. Stone On One-Parameter Unitary Groups in Hilbert Space , 1932 .

[4]  E. L. Linear Transformations in Hilbert Space: and their Applications to Analysis , 1933, Nature.

[5]  K. Yosida On the group embedded in the metrical complete ring , 1936 .

[6]  E. C. Titchmarsh,et al.  The Laplace Transform , 1991, Heat Transfer 1.

[7]  Kôsaku Yosida,et al.  On the differentiability and the representation of one-parameter semi-group of linear operators. , 1948 .

[8]  K. Yosida An operator-theoretical treatment of temporally homogeneous Markoff process , 1949 .

[9]  R. Phillips,et al.  Perturbation theory for semi-groups of linear operators , 1953 .

[10]  R. Phillips,et al.  DISSIPATIVE OPERATORS AND HYPERBOLIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS , 1959 .

[11]  R. Phillips Semi-groups of positive contraction operators , 1962 .

[12]  W. Rudin,et al.  Fourier Analysis on Groups. , 1965 .

[13]  Angus E. Taylor General theory of functions and integration , 1965 .

[14]  M. Sova,et al.  Cosine operator functions , 1966 .

[15]  M. Atiyah,et al.  Seminar on the Atiyah-Singer Index Theorem. , 1968 .

[16]  I. Vidav Spectra of perturbed semigroups with applications to transport theory , 1970 .

[17]  Zbigniew Semadeni,et al.  Banach spaces of continuous functions , 1971 .

[18]  E. Stein,et al.  Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .

[19]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .

[20]  A. Pazy On the Applicability of Lyapunov’s Theorem in Hilbert Space , 1972 .

[21]  H. Stewart Generation of analytic semigroups by strongly elliptic operators , 1974 .

[22]  C. Travis,et al.  Existence and stability for partial functional differential equations , 1974 .

[23]  H. H. Schaefer Banach Lattices and Positive Operators , 1975 .

[24]  R. Triggiani On the stabilizability problem in Banach space , 1975 .

[25]  The approximation of flows , 1977 .

[26]  J. Voigt On the perturbation theory for strongly continuous semigroups , 1977 .

[27]  D. Russell Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .

[28]  R. D. Richtmyer,et al.  Linear Operators in a Hilbert Space , 1978 .

[29]  田辺 広城,et al.  Equations of evolution , 1979 .

[30]  Barry Simon,et al.  Methods of modern mathematical physics. III. Scattering theory , 1979 .

[31]  L. Pâquet Semi-groupes generalises et equations d’evolution , 1979 .

[32]  Jürgen Voigt,et al.  A perturbation theorem for the essential spectral radius of strongly continuous semigroups , 1980 .

[33]  W. Schempp,et al.  Einführung in die harmonische Analyse , 1980 .

[34]  J. Weidmann Linear Operators in Hilbert Spaces , 1980 .

[35]  A. J. Pritchard,et al.  Stability and Stabilizability of Infinite-Dimensional Systems , 1981 .

[36]  M. Wolff A Remark on the Spectral Bound of the Generator of Semigroups of Positive Operators with Applications to Stability Theory , 1981 .

[37]  A. Sinclair Continuous Semigroups in Banach Algebras , 1982 .

[38]  Positivity in Time Dependent Linear Transport Theory , 1984 .

[39]  W. Ruppert Compact Semitopological Semigroups: An Intrinsic Theory , 1984 .

[40]  J. Voigt Spectral properties of the neutron transport equation , 1985 .

[41]  Eugenio Sinestrari,et al.  On the abstract Cauchy problem of parabolic type in spaces of continuous functions , 1985 .

[42]  G. Webb Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[43]  G. Webb An operator-theoretic formulation of asynchronous exponential growth , 1987 .

[44]  K. Taira,et al.  Diffusion Processes and Partial Differential Equations , 1988 .

[45]  W. Ruess,et al.  Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity , 1989 .

[46]  R. Triggiani,et al.  Lack of uniform stabilization for noncontractive semigroups under compact perturbation , 1989 .

[47]  Masahiro Yamamoto,et al.  Controllability and observability of linear retarded systems in Banach spaces , 1989 .

[48]  V. Wróbel Stability and spectra ofC0-semigroups , 1989 .

[49]  F. Neubrander Integrated semigroups and their application to complete second order cauchy problems , 1989 .

[50]  George Weiss,et al.  Admissibility of unbounded control operators , 1989 .

[51]  Liang Jin,et al.  On complete second order linear differential equations in Banach spaces. , 1990 .

[52]  The resolvent growth assumption for semigroups on Hilbert spaces , 1990 .

[53]  D. Russell A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques , 1991 .

[54]  Über die Stabilität von dissipativen Wellengleichungen , 1992 .

[55]  W. Ruess,et al.  Ergodic theorems for semigroups of operators , 1992 .

[57]  Jürgen Voigt,et al.  On the convex compactness property for the strong operator topology , 1992 .

[58]  On the Existence of Feller Semigroups With Boundary Conditions , 1992 .

[59]  A Hille-Yosida theorem for the higher-order abstract Cauchy problem , 1992 .

[60]  R. Rebarber Conditions for the equivalence of internal and external stability for distributed parameter systems , 1993, IEEE Trans. Autom. Control..

[61]  J. Prüss Evolutionary Integral Equations And Applications , 1993 .

[62]  Michael Renardy,et al.  On the linear stability of hyperbolic PDEs and viscoelastic flows , 1994 .

[63]  René T. Rau,et al.  Hyperbolic evolution semigroups on vector valued function spaces , 1994 .

[64]  R. Schnaubelt,et al.  A Spectral Characterization of Exponentially Dichotomic and Hyperbolic Evolution Families , 1994 .

[65]  B. Straub Fractional powers of operators with polynomially bounded resolvent and the semigroups generated by them , 1994 .

[66]  Q. Zheng Strongly continuous M, N-families of bounded operators , 1994 .

[67]  Multiplicative Perturbations of C0-Semigroups and Some Applications to Step Responses and Cumulative Outputs , 1995 .

[68]  R. Rebarber Exponential Stability of Coupled Beams with Dissipative Joints: A Frequency Domain Approach , 1995 .

[69]  Gilead Tadmor,et al.  Neutral Equations and Associated Semigroups , 1995 .

[70]  Lutz Weis,et al.  On the asymptotic behaviour of a semigroup of linear operators , 1995 .

[71]  On the stability of differentiability of semigroups , 1995 .

[72]  The stability of positive semigroups on _{} spaces , 1995 .

[73]  平良 和昭 Analytic semigroups and semilinear initial boundary value problems , 1995 .

[74]  Roland Schnaubelt,et al.  The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions , 1996 .

[75]  Rainer Nagel,et al.  IDENTIFICATION OF EXTRAPOLATION SPACES FOR UNBOUNDED OPERATORS , 1996 .

[76]  Jianhong Wu Theory and Applications of Partial Functional Differential Equations , 1996 .

[77]  E. Sinestrari Interpolation and Extrapolation Spaces in Evolution Equations , 1996 .

[78]  Asymptotics of a new population model with quiescence , 1996 .

[79]  E. Vesentini Spectral Properties of Weakly Asymptotically Almost Periodic Semigroups , 1997 .

[80]  Lloyd N. Trefethen,et al.  Pseudospectra of Linear Operators , 1997, SIAM Rev..

[81]  田辺 広城,et al.  Functional analytic methods for partial differential equations , 1997 .

[82]  On the existence of Feller semigroups with boundary conditions. III , 1997 .

[83]  H. Thieme Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth , 1998 .

[84]  Horst R. Thieme,et al.  Balanced exponential growth of operator semigroups , 1998 .

[85]  R. Schilling Subordination in the sense of Bochner and a related functional calculus , 1998, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[86]  A short proof for the stability theorem for positive semigroups on $L , 1998 .

[87]  Positivity and Stability for a Population Equation with Diffusion on 1 , 1998 .

[88]  Jin Liang,et al.  The Cauchy Problem for Higher Order Abstract Differential Equations , 1999 .

[89]  Evolution Semigroups and Product Formulas for Nonautonomous Cauchy Problems , 2000 .