Embedding of RCD?(K,N) spaces in L2 via eigenfunctions
نویسندگان
چکیده
In this paper we study the family of embeddings ?t a compact RCD?(K,N) space (X,d,m) into L2(X,m) via eigenmaps. Extending part classical results [10], [11] known for closed Riemannian manifolds, prove convergence as t?0 rescaled pull-back metrics ?t?gL2 in induced by ?t. Moreover discuss behavior with respect to measured Gromov-Hausdorff and t. Applications include quantitative Lp-convergence noncollapsed setting all p<?, result new even manifolds Alexandrov spaces.
منابع مشابه
Embedding measure spaces
For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable. The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space. Under certain conditions the construction simplifies. Examples are given when this simplification o...
متن کاملApproximation of eigenfunctions in kernel-based spaces
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the ”native” Hilbert space H in which they are reproducing. Continuous kernels on compact domains have an expansion into eigenfunctions that are both L2-orthonormal and orthogonal in H (Mercer expansion). This paper examines the corresponding eigenspaces and proves that they have optimality p...
متن کاملembedding measure spaces
for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable. the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space. under certain conditions the construction simplifies. examples are given when this simplification o...
متن کاملEmbedding normed linear spaces into $C(X)$
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
متن کاملLocal Parametrizations via Laplacian Eigenfunctions
Eigenfunction methods for mapping high dimensional data sets into lower dimensional spaces are useful in a broad range of applications. In particular, a recent paper by Jones et al [2] shows that eigenfunctions of the Laplacian operator give a good local coordinate system under very general conditions. Here I outline the proof of the theorem and explore its use in cryo-electron microscopy.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2021
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2021.108968