Dirichlet forms and critical exponents on fractals
نویسندگان
چکیده
منابع مشابه
A trace theorem for Dirichlet forms on fractals
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to their boundaries, where boundaries mean the triangles and rectangles which confine gaskets and carpets. As an application, we construct diffusion processes on ...
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In this summary we want to present the main results which are contained in the author’s “Habilitationsschrift” (dissertation). It has been written in German and has been submitted to the Faculty of Mathematics and Physics of the University of Bayreuth. Moreover we want to comment on these results, sketch some of the ideas how to prove them and give some background information. For the reader’s ...
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In this paper we explore the metric-measure spaces introduced by Laakso in 2000. Building upon the work of Barlow and Evans we are able to show the existence of a large supply of Dirichlet forms, or alternatively Markov Processes, on these spaces. The construction of Barlow and Evans allows us to justify the use of a quantum graph perspective to identify and describe a Laplacian operator genera...
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We introduce the concept of index for regular Dirichlet forms by means of energy measures, and discuss its properties. In particular, it is proved that the index of strong local regular Dirichlet forms is identical with the martingale dimension of the associated diffusion processes. As an application, a class of self-similar fractals is taken up as an underlying space. We prove that first-order...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2019
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/8004