Gaussian estimates and holomorphy of semigroups

We show that if a selfadjoint semigroup T on L2(Q) satisfies a Gaussian estimate IT(t)fI o is the Gaussian semigroup on L2(RN) and Q is an open set of RN ), then T defines a holomorphic semigroup of angle ' on LP(Q), 1 < p < o0 . We obtain by duality the same result on Co(Q) . Applications to uniformly elliptic operators and Schrodinger operators are given.

[1]  Société de mathématiques appliquées et industrielles,et al.  Introduction aux problèmes d'évolution semi-linéaires , 1990 .

[2]  Wolfgang Arendt,et al.  Absorption semigroups and dirichlet boundary conditions , 1993 .

[3]  J. V. Casteren,et al.  ON SPECTRAL THEORY OF SELFADJOINT FELLER GENERATORS , 1989 .

[4]  J. Roth.  Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues , 1976 .

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

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

[7]  El Maati Ouhabaz,et al.  Invariance of closed convex sets and domination criteria for semigroups , 1996 .

[8]  M. Reed.  Methods of Modern Mathematical Physics. I: Functional Analysis , 1972 .

[9]  E. Hille.  Functional Analysis And Semi-Groups , 1948 .

[10]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[11]  Zhi-Ming Ma,et al.  Feynman-Kac semigroups in terms of signed smooth measures , 1991 .

[12]  E. Davies,et al.  Heat kernels and spectral theory , 1989 .

[13]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[14]  H. Amann.  Dual semigroups and second order linear elliptic boundary value problems , 1983 .

[15]  J. Goldstein.  Semigroups of Linear Operators and Applications , 1985 .

[16]  R. Nagel,et al.  One-parameter Semigroups of Positive Operators , 1986 .

[17]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[18]  H. Bruce Stewart,et al.  Generation of analytic semigroups by strongly elliptic operators under general boundary conditions , 1980 .

[19]  P. Stollmann,et al.  Perturbation of Dirichlet forms by measures , 1996 .