Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space

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Dan Lemle , Ludovic; Wu , Liming;
  • Publisher: HAL CCSD
  • Subject: mass transport equation | 2000 AMS Subject Classification} Primary: 47D03, 47F05 Secondary: 60J60 | $L^\infty$-uniqueness | [ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA] | [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA] | 47D03, 47F05 (Primary) | 60J60 (Secondary) | Mathematics - Functional Analysis | $C_0$-semigroups
    arxiv: Mathematics::Functional Analysis | Mathematics::Operator Algebras

The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex... View more
  • References (10)

    [Eb'97] Eberle, A. Uniquenees and non-uniqueness of singular diffusion operators. Doctor-thesis, Bielefeld, 1997.

    [Fa'68] Fattorini, H.O. Ordinary differential equations in linear topological spaces. J. Diff. Eq., 5(1968), 72-105.

    [Ko'64] Komatsu, H. Semigroups of operators in locally convex spaces. J. Math. Soc. Japan, 16(1964), 230-262.

    [K˜o'68] Ko˜mura, T. Semigroups of Operators in Locally Convex Spaces. J. Funct. Anal., 2(1968), 258-296.

    [Mi'59] Miyadera, I. Semi-groups of operators in Fr´echet space and applications to partial differential equations. Tˆohocu Math. J., 11(1959), 162-183.

    [Mo'69] Moore, R.T. Banach algebras of operators in locally convex spaces. Bull. Amer. Math. Soc., 75(1969), 68-73.

    [Wu'98] Wu, L. Uniqueness of Schr¨odinger Operators Restricted in a Domain. J. Funct. Anal., (2)153(1998), 276-319.

    [Wu'99] Wu, L. Uniqueness of Nelson's diffusions. Probab. Theory Relat. Fields, 114(1999), 549-585.

    [WZ'06] Wu, L., Zhang, Y. A new topological approach to the L∞-uniqueness of operators and the L1-uniqueness of Fokker-Planck equations. J. Funct. Anal., 241(2006), 557-610.

    [Yo'71] Yosida, K. Functional Analysis. Springer Verlag, New York, 1971.

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