Abstract
Local Dirichlet forms have developped into an important tool for the nonperturbative treatment of quantum dynamics and diffusion processes. With a view towards quantum field theory it is desirable to extend the formalism to infinite dimensional (”configuration”) spaces. As a starting point we choose the L2 space (L2) over the White Noise measure. More general measures are constructed by first embedding (L2) into a triple (S) ⊂ (L2) ⊂ (C)*. Positive elements of (S)* are measures. We call a positive generalized functional admissible if the corresponding measure ν gives rise to a closable energy form on (L2) ν . Any admissible generalized functional gives rise to a Markovian form in the sense of Fukushima.
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© 1990 Kluwer Academic Publishers
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Streit, L. (1990). Energy Forms in Terms of White Noise. In: Albeverio, S., Blanchard, P., Testard, D. (eds) Stochastics, Algebra and Analysis in Classical and Quantum Dynamics. Mathematics and Its Applications, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7976-8_13
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DOI: https://doi.org/10.1007/978-94-011-7976-8_13
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