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Creators/Authors contains: "Kumagai, Takashi"

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  1. ; ; (, Annales Fennici Mathematici)
    In the context of a metric measure space \((X,d,\mu)\), we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of the Besov space \(B^\theta_{p,p}(X)\) is \(k>1\), then \(X\) can be decomposed into \(k\) number of irreducible components (Theorem 1.1). Note that \(\theta\) may be bigger than \(1\), as our framework includes fractals. We also provide sufficient conditions under which the dimension of the Besov space is 1. We introduce critical exponents \(\theta_p(X)\) and \(\theta_p^{\ast}(X)\) for the Besov spaces. As examples illustrating Theorem 1.1, we compute these critical exponents for spaces \(X\) formed by glueing copies of \(n\)-dimensional cubes, the Sierpiński gaskets, and of the Sierpiński carpet. 
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    Free, publicly-accessible full text available January 2, 2026
  2. ; ; ; ; (, Springer)
    This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups. 
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    Accepted Manuscript Full Text Available
  3. ; ; ; ; (, Annales de l'Institut Fourier)
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  4. ; ; ; (, Probability Theory and Related Fields)
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  5. ; ; ; (, Oberwolfach Reports)
    null (Ed.)
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  6. ; ; ; ; ; (, Nano Letters)
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