In the past Kazuhiro Kuwae has collaborated on articles with Patrick J. Fitzsimmons. One of their most recent publications is Non-symmetric perturbations of symmetric Dirichlet forms. Which was published in journal Journal of Functional Analysis.

More information about Kazuhiro Kuwae research including statistics on their citations can be found on their Copernicus Academic profile page.

Kazuhiro Kuwae's Articles: (2)

Non-symmetric perturbations of symmetric Dirichlet forms

AbstractWe provide a path-space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local Dirichlet form. The representation is a combination of Feynman–Kac and Girsanov formulas, and extends previously known results in the framework of symmetric diffusion processes through the use of the Hardy class of smooth measures, which contains the Kato class of smooth measures.

Kato class measures of symmetric Markov processes under heat kernel estimates

AbstractWe establish the coincidence of two classes of Kato class measures in the framework of symmetric Markov processes admitting upper and lower estimates of heat kernel under mild conditions. One class of Kato class measures is defined by way of the heat kernel, another is defined in terms of the Green kernel depending on some exponents related to the heat kernel estimates. We also prove that pth integrable functions on balls with radius 1 having a uniformity of its norm with respect to centers are of Kato class if p is greater than a constant related to the estimate under the same conditions. These are complete extensions of some results for the Brownian motion on Euclidean space by Aizenman and Simon. Our result can be applicable to many examples, for instance, symmetric (relativistic) stable processes, jump processes on d-sets, Brownian motions on Riemannian manifolds, diffusions on fractals and so on.

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