Geodesic
Generalized Resolvent Equations and Unsymmetric Dirichlet Spaces
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1111-1141

Voir la notice de l'article provenant de la source Cambridge University Press

Let (X, , μ) and (X, , μ′) be measure spaces with the measures μ and μ′ totally finite. Suppose {Uλ: λ > 0} is a family of positive (i.e., φ ≧ 0 ⇒ Uλφ ≧ 0) continuous linear operators from L 2(X, dμ′) to L 2(X,dμ) with the following additional properties: if φ ≧ 0 then Uλφ is non-decreasing as λ increases, while λ −1 Uλφ is nonincreasing.A family {Mλ:λ > 0} of continuous linear operators from L 2(X, dμ) to L 2(X, dμ′) satisfies the “generalized resolvent equation” relative to {U λ} if (0.1) for positive λ and v. If Uλ = λI, then (0.1) is just the well-known resolvent equation. The family {Mλ } is called submarkov if Mλ is a positive operator and (0.2) it is conservative if (0.3) 
Elliott, Joanne. Generalized Resolvent Equations and Unsymmetric Dirichlet Spaces. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1111-1141. doi: 10.4153/CJM-1981-085-7
@article{10_4153_CJM_1981_085_7,
     author = {Elliott, Joanne},
     title = {Generalized {Resolvent} {Equations} and {Unsymmetric} {Dirichlet} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {1111--1141},
     year = {1981},
     volume = {33},
     number = {5},
     doi = {10.4153/CJM-1981-085-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-085-7/}
}
TY  - JOUR
AU  - Elliott, Joanne
TI  - Generalized Resolvent Equations and Unsymmetric Dirichlet Spaces
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 1111
EP  - 1141
VL  - 33
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-085-7/
DO  - 10.4153/CJM-1981-085-7
ID  - 10_4153_CJM_1981_085_7
ER  - 
%0 Journal Article
%A Elliott, Joanne
%T Generalized Resolvent Equations and Unsymmetric Dirichlet Spaces
%J Canadian journal of mathematics
%D 1981
%P 1111-1141
%V 33
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-085-7/
%R 10.4153/CJM-1981-085-7
%F 10_4153_CJM_1981_085_7

[1] 1. Feller, W., On boundaries and lateral conditions for the Kolmogorov differential equations, Annals of Mathematics 65 (1957), 527–570. Google Scholar

[2] 2. Fukushima, M., On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densities, Journal of the Mathematical Society of Japan 21 (1969), 58–93. Google Scholar

[3] 3. Kunita, H., Sub-markov semigroups in Banach lattices, Proceedings of the international conference on functional analysis and related topics (1969), Tokyo, 332–343. Google Scholar

[4] 4. Kunita, H., General boundary conditions for multidimensional diffusion processes, J. Math. Kyoto Univ. 10 (1970), 273–335. Google Scholar

Cité par Sources :