Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry

By K. Kuwae, T. Shioya. 2003

180 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/40e86215a8bc989bc472f710a42ed4a98745677a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Luigi Ambrosio
2. Karl‐Theodor Sturm
3. Emanuel Milman
4. Nicola Gigli
5. Shouhei Honda
6. Max-K. von Renesse
7. A. V. Kolesnikov
8. David Tewodrose

In Astronomy and Astrophysics

1. Luigi Ambrosio
2. Shouhei Honda
3. Karl‐Theodor Sturm
4. David Tewodrose
5. A. V. Kolesnikov
6. Radoslaw K. Wojciechowski
7. Max-K. von Renesse
8. Nicola Gigli

Citations in the corpus

• On the geometry of metric measure spaces. II (2006, background): “Yet another convergence concept was proposed by K. Kuwae and T. Shioya [ KS03 ] extending the concept of -convergence and Mosco convergence towards a notion of convergence of operators (or Dirichlet forms or heat semigroups) on varying spaces.”
• A note on self-adjoint extensions of the Laplacian on weighted graphs (2012, background): “On the other hand, if the manifold is geodesically incomplete, the Laplacian is not essentially self-adjoint in general; however, if the Cauchy boundary, which is the difference between the completion of the manifold and the manifold itself, is “small” in some sense, then it is essentially self-adjo”
• Ricci curvature and $L^p$-convergence (2012, methodology): “Kuwae-Shioya proved the existence of the Dirichlet Laplacian on L(2)(BR(m∞)) and similar continuities for noncompact case in [38].”
• Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces (2017, background): “Other good formulations of L2-convergence, in connection with mGH-convergence, can be found in [30,39].”
• Convergence of pointed non‐compact metric measure spaces and stability of Ricci curvature bounds and heat flows (2013, unknown): “6 in [25].”
• Particle approximation of the Wasserstein diffusion (2007, background): “Proposition 3.4 is proved by showing that the sequence of generating Dirichlet forms N ·EN of (gN· ) on L2(ΣN , qN ) converges to E on L2(G, Q) in the generalized Mosco sense of Kuwae and Shioya, allowing for varying base L2-spaces.”
• Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures (2006, background): “General results on Mosco convergence Following [20] we define convergence of Hilbert spaces, vectors, operators, and forms.”
• Local spectral convergence in RCD∗(K,N) spaces (2017, background): “ues still satisfies the Dirichlet boundary condition is raised, but the main result of that paper, namely the convergence of the heat kernels, is proved independently of an answer to this question. In [KS03], the spectral convergence as well as the Mosco convergence of the local Cheeger energies with”