Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 10391064 (1999) 

Representation Formulas for NonSymmetric Dirichlet FormsS. MataloniUniv. Roma Tor Vergata, Dept. Math., Via della Ricerca Scientifica, 00133 Roma, Italy; \ Mataloni@mat.uniroma2.itAbstract: As wellknown, for $X$ a given locally compact separable Hausdorff space, $m$ a positive Radon measure on $X$ with supp$\,[m] = X$ and $C_0(X)$ the space of all continuous functions with compact support on $X$ the Beurling and Deny formula states that any regular Dirichlet form $(\tilde\E,D(\tilde \E))$ on $\LX$ can be expressed as $$ \tilde\E(u,v) = \tilde\E^c(u,v) + \iX uv k(dx) + \id(u(x)u(y))((v(x)  v(y))\tilde j(dx,dy) $$ for all $u,v \in D(\tilde\E) \cap C_0(X)$ where the symmetric Dirichlet form $\tilde\E^c$, the symmetric measure $\tilde j(dx,dy)$ and the measure $k(dx)$ are uniquely determined by $\tilde\E$. It is our aim to prove this formula in the nonsymmetric case. For this we consider certain families of nonsymmetric Dirichlet forms of diffusion type and show that these forms admit an integral representation involving a measure that enjoys some important functional properties as well as in the symmetric case. Keywords: nonsymmetric Dirichlet forms, BeurlingDeny formula, diffusion forms, energy measures, differentiation formulas, differential operators Classification (MSC2000): 28A99, 31C25, 35J70 Full text of the article:
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